Szent-Györgyi was born in Budapest, Hungary. His father, Miklós Szent-Györgyi, was a landowner. His mother, Jozefin, was a daughter of József Lenhossék and a sister of Mihály Lenhossék; both of these men were Professors of Anatomy at the University of Budapest. Szent-Györgyi began his studies at the Budapest Medical School, but soon became bored with classes and began research in his uncle's anatomy lab. His studies were interrupted in 1914 to serve as an army medic in World War I. In 1916, disgusted with the war, Szent-Györgyi shot himself in the arm, claimed to be wounded from enemy fire, and was sent home on medical leave. He was then able to finish his medical education and receive his MD in 1917. He married Kornélia Demény, the daughter of the Hungarian Postmaster General that same year. She accompanied him to his next position at an army clinic in northern Italy.

After the war, Szent-Györgyi began his research career in Pressburg (Hungarian: Pozsony, today: Bratislava). When the city became part of Czechoslovakia in January 1919, he left the town as did a portion of the Hungarian population. He switched universities several times over the next few years, finally ending up at the University of Groningen, where his work focused on the chemistry of cellular respiration. This work landed him a position as a Rockefeller Foundation fellow at Cambridge University. He received his PhD from Cambridge in 1927 for his work on isolating what he then called "hexuronic acid" from adrenal gland tissue.

He accepted a position at the University of Szeged in 1931. There, Szent-Györgyi and his research fellow Joseph Svirbely found that "hexuronic acid" was actually vitamin C (the L-enantiomer of ascorbic acid) and noted its anti-scorbutic activity. In some experiments they used paprika as the source for their vitamin C. Also during this time, Szent-Györgyi continued his work on cellular respiration, identifying fumaric acid and other steps in what would become known as the Krebs cycle.

In 1937, he received the Nobel Prize in Physiology or Medicine "For his discoveries in connection with the biological combustion process with special reference to vitamin C and the catalysis of fumaric acid". In 1938, he began work on the biophysics of muscle movement. He found that muscles contain actin, which when combined with the protein myosin and the energy source ATP, contract muscle fibers.

As fascists gained control of politics in Hungary, Szent-Györgyi helped his Jewish friends escape from the country. During World War II, he joined the Hungarian resistance movement. Although Hungary was allied with the Axis Powers, the Hungarian prime minister Miklós Kállay sent Szent-Györgyi to Cairo in 1944 under the guise of a scientific lecture to begin secret negotiations with the Allies. The Germans learned of this plot, and Adolf Hitler himself issued a warrant for the arrest of Szent-Györgyi. He escaped house arrest and spent 1944 to 1945 as a fugitive from the Gestapo.

After the war, Szent-Györgyi was well-recognized as a public figure and there was some speculation that he might become President of Hungary, should the Soviets permit it. Szent-Györgyi established a lab at the University of Budapest and became head of the biochemistry department there. He was elected as a member of Parliament and helped re-establish the Academy of Sciences. Dissatisfied with the Communist rule of Hungary, he emigrated to the United States in 1947.

In 1947, Szent-Györgyi established the Institute for Muscle Research at the Marine Biological Laboratory in Woods Hole, Massachusetts, with financial support from Hungarian businessman Stephen Rath. However, Szent-Györgyi still faced funding difficulties for several years, due to his foreign status and former association with the government of a Communist nation. In 1948, he received a research position with the National Institutes of Health (NIH) in Bethesda, Maryland, and began dividing his time between there and Woods Hole. In 1950, grants from the Armour Meat Company and the American Heart Association allowed him to establish the Institute for Muscle Research.

During the 1950s, Szent-Györgyi began using electron microscopes to study muscles at the subunit level. He received the Lasker Award in 1954. In 1955, he became a naturalized citizen of the United States. He became a member of the National Academy of Sciences in 1956.

In the late 1950s, Szent-Györgyi developed a research interest in cancer and developed ideas on applying the theories of quantum physics to the biochemistry of cancer. The death of Rath, who had acted as the financial administrator of the Institute for Muscle Research, left Szent-Györgyi in a financial mess. Szent-Györgyi refused to submit government grants which required him to provide minute details on exactly how he intended to spend the research dollars and what he expected to find. After Szent-Györgyi commented on his financial hardships in a 1971 newspaper interview, attorney Franklin Salisbury contacted him and later helped him establish a private nonprofit organization, the National Foundation for Cancer Research. Late in life, Szent-Györgyi began to pursue free radicals as a potential cause of cancer. He came to see cancer as being ultimately an electronic problem at the molecular level. In 1974, reflecting his interests in quantum physics, he proposed the term "syntropy" replace the term "negentropy". Ralph Moss, a protegé of his in the years he performed his cancer research, wrote a biography entitled: "Free Radical: Albert Szent-Gyorgyi and the Battle over Vitamin C".

He died in Woods Hole, Massachusetts on October 22, 1986.