Alexander Michael Prochoroff was born on 11 July 1916 at Russell Road, Peeramon, Queensland, Australia (now 322 Gadaloff Road, Butchers Creek, situated about 30 km from Atherton), to Mikhail Ivanovich Prokhorov and Maria Ivanovna (née Mikhailova), Russian revolutionaries who had emigrated from Russia to escape repression by the tsarist regime. As a child he attended Butchers Creek State School.
In 1923, after the October Revolution and the Russian Civil War, the family returned to Russia. In 1934, Prokhorov entered the Saint Petersburg State University to study physics. He was a member of the Komsomol from 1930 to 1944. Prokhorov graduated with honors in 1939 and moved to Moscow to work at the Lebedev Physical Institute, in the oscillations laboratory headed by academician N. D. Papaleksi. His research there was devoted to propagation of radio waves in the ionosphere. At the onset of World War II in the Soviet Union, in June 1941, he joined the Red Army. During World War II, Prokhorov fought in the infantry, was wounded twice in battles, and was awarded three medals, including the Medal For Courage in 1946. He was demobilized in 1944 and returned to the Lebedev Institute where, in 1946, he defended his Ph.D. thesis on "Theory of Stabilization of Frequency of a Tube Oscillator in the Theory of a Small Parameter".