Minc was born into a middle class Jewish family; his parents were Oskar Minc and Stefania née Fajersztajn. Minc joined the Communist Party of Poland, which was eliminated by the Comintern before World War II. He spent the wartime in the Soviet Union, where he participated in the founding and activities of the Union of Polish Patriots. As an officer in the Polish People's Army, he fought on the Eastern Front and received military decorations, including the Virtuti Militari. Between 1944 and 1956, he was a member of the Politburo of the Polish Workers' Party (PPR) and then the Polish United Workers' Party (PZPR).
Minc was a top-ranking member of Bolesław Bierut's political apparatus from 1948, together with Jakub Berman. He served as minister of industry and commerce and deputy prime minister for economic affairs during the Stalinist period in the Polish People's Republic (until 1956). Minc participated in Władysław Gomułka's meetings with Joseph Stalin at the Kremlin. Stalin personally assigned Minc first to the Ministry of Industry and then to the Ministry of Transportation of Poland in 1949. Minc was one of the main architects of Poland's Six-Year Plan, implemented in 1950. His wife, Julia, was editor-in-chief of the Polish Press Agency until 1954.
At a celebration at Wrocław for the so-called Recovered Territories, Minc acclaimed the gaining of the completely equipped previously German land with its residue of German population which and proclaimed his government's right to liquidate the remaining Germans by appropriate methods.
In 1956, Minc was removed from the Politburo and in 1959 forced to leave the PZPR altogether.
- Schatz, Jaff (1991). The Generation: The Rise and Fall of the Jewish Communists of Poland. University of California Press. p. 369.
- Andrzej Werblan, New Evidence on Poland in the Early Cold War, "Conversation between Władysław Gomułka and Stalin on 14 November 1945".
- R. M. Douglas. Orderly and Humane. The Expulsion of the Germans after the Second World War. Yale University Press. p. 258.