Born the son of a composer in St. Petersburg, Russia, Friedmann was educated at the university there. He began his scientific career in 1913 at the Pavlovsk Observatory in St. Petersburg and, after war service, was appointed professor of theoretical mechanics at Perm University in 1918. In 1920 he returned to the St. Petersburg Observatory where he became director shortly before his death from typhoid at the age of 37.

Friedmann established an early reputation for his work on atmospheric and meteorological physics. He is, however, better known for his 1922 paper on the expanding universe. This arose from work of Einstein in 1917 in which he attempted to apply his equations of general relativity to cosmology. Friedmann developed a theoretical model of the universe using Einstein's theory, in which the average mass density is constant and space has a constant curvature. Different cosmological models are possible depending on whether the curvature is zero, negative, or positive. Such models are called Friedmann universes.