He was born at Balassagyarmat, in Hungary, when his father Jakub Doubravský was temporarily stationed as a soldier there. He received his first education in the German school at Horšovský Týn in Plzeň district, made his first acquaintance with the Czech language and soon made himself fluent in it at the Německý Brod gymnasium and then studied for some time under the Jesuits at Klatovy. In 1769 he began to study philosophy at the University of Prague. In 1772 he was admitted among the Jesuits at Brno and was preparing for a Christian mission in India. However, the entire order was dissolved in the Czech lands in 1773 and Dobrovský thus returned to Prague to study theology.

After holding for some time the office of tutor for the Count Nostitz, he obtained an appointment first as vice-rector, and then as rector, in the general seminary at Hradisko (now part of Olomouc); but in 1790 he lost his post through the abolition of the seminaries throughout the Habsburg Empire, and returned as a guest to the house of the count. At this time, he wrote some of the most important works in Slavic studies, historiography and philology.

In 1792 he was commissioned by the Bohemian Academy of Sciences to visit Stockholm, Turku, St Petersburg and Moscow in search of the manuscripts which had been scattered by the Thirty Years' War; and on his return he accompanied Count Nostitz to Switzerland and Italy.

In the 1780's, Dobrovský participated in the academic life of Prague. In 1784, he helped to set up the Royal Czech Society of Sciences, and in 1818 the National Museum of what was to become Czechoslovakia and eventually the Czech Republic.

However, his reason began to give way in 1795, and in 1801 he had to be confined in a lunatic asylum; but by 1803 he had completely recovered. The rest of his life was mainly spent either in Prague or at the country seats of his friends Counts Nostitz and Czernin; but his death took place in Brno, where he had gone in 1828 to study in the local libraries.

While his fame rests chiefly on his labours in Slavonic philology his botanical studies are not without value in the history of the science.

Between 1948 and 1968 the Czech poet Vladimír Holan lived in the so called "Dobrovský´s House" at Kampa, often saying that the Blue Abbé (a nickname under which Dobrovský was known) would sometimes visit him.