He was born in Dessau, the son of the Romantic poet Wilhelm Müller, whose verse Franz Schubert had set to music in his song - cycles Die schöne Müllerin and Winterreise. Max Müller's mother, Adelheide Müller, was the eldest daughter of a chief minister of Anhalt - Dessau. Müller knew Felix Mendelssohn and had Carl Maria von Weber as a godfather.

In 1841 he entered Leipzig University, where he left his early interest in music and poetry in favour of philosophy. Müller received his Ph.D.in 1843 for a dissertation on Spinoza's Ethics. He also displayed an aptitude for languages, learning the Classical languages Greek and Latin, as well as Arabic, Persian and Sanskrit. In 1844 Müller went to Berlin to study with Friedrich Schelling. He began to translate the Upanishads for Schelling, and continued to research Sanskrit under Franz Bopp, the first systematic scholar of the Indo - European languages. Schelling led Müller to relate the history of language to the history of religion. At this time, Müller published his first book, a German translation of the Hitopadesa, a collection of Indian fables.

In 1845, Müller moved to Paris to study Sanskrit under Eugène Burnouf. It was Burnouf who encouraged him to publish the complete Rig Veda in Sanskrit, using manuscripts available in England.

Müller moved to England in 1846 in order to study Sanskrit texts in the collection of the East India Company. He supported himself at first with creative writing, his novel German Love being popular in its day. Müller's connections with the East India Company and with Sanskritists based at Oxford University led to a career in Britain, where he eventually became the leading intellectual commentator on the culture of India, which Britain controlled as part of its Empire. This led to complex exchanges between Indian and British intellectual culture, especially through Müller's links with the Brahmo Samaj. He became a member of Christ Church, Oxford, in 1851, when he gave his first series of lectures on comparative philology. He gained appointments as Taylorian Professor of Modern European Languages in 1854. Defeated in the 1860 competition for the tenured Chair of Sanskrit, he later became Oxford's first Professor of Comparative Theology (1868 – 1875), at All Souls College.

Müller attempted to formulate a philosophy of religion that addressed the crisis of faith engendered by the historical and critical study of religion by German scholars on the one hand, and by the Darwinian revolution on the other. Müller was wary of Darwin's work on human evolution, and attacked his view of the development of human faculties. His work was taken up by cultural commentators such as his friend John Ruskin, who saw it as a productive response to the crisis of the age (compare Matthew Arnold's "Dover Beach"). He analyzed mythologies as rationalizations of natural phenomena, primitive beginnings that we might denominate "protoscience" within a cultural evolution; Müller's "anti - Darwinian" concepts of the evolution of human cultures are among his least lasting achievements.

Müller shared many of the ideas associated with Romanticism, which coloured his account of ancient religions, in particular his emphasis on the formative influence on early religion of emotional communion with natural forces.

Müller's Sanskrit studies came at a time when scholars had started to see language development in relation to cultural development. The recent discovery of the Indo - European (IE) language group had started to lead to much speculation about the relationship between Greco - Roman cultures and those of more ancient peoples. In particular the Vedic culture of India was thought to have been the ancestor of European Classical cultures, and scholars sought to compare the genetically related European and Asian languages in order to reconstruct the earliest form of the root language. The Vedic language, Sanskrit, was thought to be the oldest of the IE languages. Müller therefore devoted himself to the study of this language, becoming one of the major Sanskrit scholars of his day. Müller believed that the earliest documents of Vedic culture should be studied in order to provide the key to the development of pagan European religions, and of religious belief in general. To this end, Müller sought to understand the most ancient of Vedic scriptures, the Rig - Veda.

Müller was greatly impressed by Ramakrishna Paramhansa, his contemporary and proponent of Vedantic philosophy, and authored several essays and books on him.

A 1907 study of Müller's inaugural Hibbert Lecture of 1878 was made by one of his contemporaries, D. Menant. It argued that a crucial role was played by Müller and social reformer Behramji Malabari in initiating debate on child marriage and widow remarriage questions in India.

For Müller, the study of the language had to relate to the study of the culture in which it had been used. He came to the view that the development of languages should be tied to that of belief systems. At that time the Vedic scriptures were little known in the West, though there was increasing interest in the philosophy of the Upanishads. Müller believed that the sophisticated Upanishadic philosophy could be linked to the primitive henotheism of early Vedic Brahmanism from which it evolved. He had to travel to London in order to look at documents held in the collection of the British East India Company. While there he persuaded the company to allow him to undertake a critical edition of the Rig - Veda, a task he pursued doggedly over many years (1849 – 1874), and which resulted in the critical edition for which he is most remembered.

For Müller, the culture of the Vedic peoples represented a form of nature worship, an idea clearly influenced by Romanticism. He saw the gods of the Rig - Veda as active forces of nature, only partly personified as imagined supernatural persons. From this claim Müller derived his theory that mythology is 'a disease of language'. By this he meant that myth transforms concepts into beings and stories. In Müller's view 'gods' began as words constructed in order to express abstract ideas, but were transformed into imagined personalities. Thus the Indo - European father - god appears under various names: Zeus, Jupiter, Dyaus Pita. For Müller all these names can be traced to the word 'Dyaus', which he understands to imply 'shining' or 'radiance'. This leads to the terms 'deva', 'deus', 'theos' as generic terms for a god, and to the names 'Zeus' and 'Jupiter' (derived from deus - pater). In this way a metaphor becomes personified and ossified. This aspect of Müller's thinking closely resembled the later ideas of Nietzsche.

Nevertheless Müller's work contributed to the developing interest in Aryan culture which set Indo - European ('Aryan') traditions in opposition to Semitic religions. He was deeply saddened by the fact that these later came to be expressed in racist terms. This was far from Müller's own intention. For Müller the discovery of common Indian and European ancestry was a powerful argument against racism, arguing that "an ethnologist who speaks of Aryan race, Aryan blood, Aryan eyes and hair, is as great a sinner as a linguist who speaks of a dolichocephalic dictionary or a brachycephalic grammar" and that "the blackest Hindus represent an earlier stage of Aryan speech and thought than the fairest Scandinavians".

In 1881, he published a translation of the first edition of Kant's Critique of Pure Reason. He agreed with Schopenhauer that this edition was the most direct and honest expression of Kant's thought. His translation corrected several errors that were committed by previous translators. In his Translator's Preface, Müller wrote, "The bridge of thoughts and sighs that spans the whole history of the Aryan world has its first arch in the Veda, its last in Kant's Critique.… While in the Veda we may study the childhood, we may study in Kant's Critique of Pure Reason the perfect manhood of the Aryan mind.… The materials are now accessible, and the English speaking race, the race of the future, will have in Kant's Critique another Aryan heirloom, as precious as the Veda — a work that may be criticised, but can never be ignored."

He was also influenced by the work Thought and Reality, of the Russian philosopher African Spir.

His wife, Georgina Adelaide (died 1916) had his papers and correspondence carefully bound; they are at the Bodleian Library, Oxford. The Goethe Institutes in India are named Max Müller Bhavan in his honour. Müller's son Wilhelm Max Müller was also an important scholar.

Müller's comparative religion was criticized as subversive of the Christian faith. According to Monsignor Munro, the Roman Catholic bishop of St Andrew's Cathedral in Glasgow, his 1888 University of Glasgow Gifford Lectures on the "science of religion" represented nothing less than "a crusade against divine revelation, against Jesus Christ and Christianity". Similar accusations had already led to Müller's exclusion from the Boden chair in Sanskrit in favour of the conservative Monier Monier - Williams. By the 1880s Müller was being courted by Charles Godfrey Leland, Helena Blavatsky and other writers who were seeking to assert the merits of "Pagan" religious traditions over Christianity. The designer Mary Fraser Tytler stated that Müller's book Chips from a German Workshop (a collection of his essays) was her "Bible", which helped her to create a multi - cultural sacred imagery.

Müller distanced himself from these developments, and remained within the Lutheran faith in which he had been brought up. He several times expressed the view that a "reformation" within Hinduism needed to occur comparable to the Christian Reformation. In his view, "if there is one thing which a comparative study of religions places in the clearest light, it is the inevitable decay to which every religion is exposed... Whenever we can trace back a religion to its first beginnings, we find it free from many blemishes that affected it in its later states". He used his links with the Brahmo Samaj in order to encourage such a reformation on the lines pioneered by Ram Mohan Roy.

In a letter to his wife, he said:

The translation of the Veda will hereafter tell to a great extent on the fate of India and on the growth of millions of souls in that country. It is the root of their religion, and to show them what the root is, I feel sure, is the only way of uprooting all that has sprung from it during the last 3000 years.

Munro had argued conversely that Müller's theories "uprooted our idea of God, for it repudiated the idea of a personal God." He made "divine revelation simply impossible, because it [his theory] reduced God to mere nature, and did away with the body and soul as we know them." Müller remained profoundly influenced by the Kantian Transcendentalist model of spirituality, and was opposed to Darwinian ideas of human development, arguing that "language forms an impassable barrier between man and beast."