Prokhorov graduated in 1939 from the faculty of physics of the Leningrad State University, where he later became a doctor of physics, mathematics, and science (1946). During World War II he served in the Russian army.

Subsequently, working at the Physics Institute of the Soviet Academy of Sciences with Nikolai Basov, Prokhorov performed fundamental work in microwave spectroscopy, which led to the development of the maser in 1955, and later the laser. Basov and Prokhorov, together with the American physicist Charles Townes, received the 1964 Nobel Prize for physics for their development of the maser principle, and were pioneers of the new science of quantum radio physics (now referred to by the broader term, quantum electronics).