Born in the village of Golovkino in Novosilsky Uyezd of Tula Governorate (now in Oryol Oblast), he spent his childhood in Chern.
[1] His younger brother Nikolai Voznesensky, also an economist, was appointed to the Politburo of the Communist Party of the Soviet Union in February 1941, becoming responsible for much of the planning of the Soviet economy and twice holding the directorship of Gosplan.
As his brother fell from favour with Joseph Stalin, in the wake of the Leningrad affair, Alexander was also arrested and tortured in August 1949.
Although Nikolai Bulganin (Minister for Defense) was friends with Alexander, he could not risk helping him, in case he would also be implicated.
[2] On August 19, 1949, he was arrested on charges of treason, participation in a counterrevolutionary organization, and anti-Soviet agitation (the Leningrad Affair).