Marian Muszkat was born in Suwałki, where he completed primary and then secondary school. In 1927 he began studies at the University of Warsaw. In Warsaw Muszkat studied law, and simultaneously worked as a clerk in factories and as a school teacher. As a student he belonged to socialist academic organizations. Muszkat was a distinctive student, thereby he soon travelled to France to continue his studies at the University of Nancy. During his stay in Nancy, Muszkat penned some new ideas about public international law, peremptory norm and international problems concerning the Third World countries. In 1931 Muszkat obtained a degree of Master of Law, and in 1936 at the same University he received a degree of Doctor of Law.
During World War II, Muszkat relocated to Vilnius first, where worked in Prawda Wileńska, and lectured at the Vilnius University. In June 1941 he evacuated to the Soviet Union. In 1941–1943 he was a clerk in a kolkhoz and a teacher in the Gzy–Orda Pedagogic Institute. In May 1943 Muszkat joined the People's Army of Poland. Having completed officers course, he served as lieutenant in the Polish 1st Tadeusz Kościuszko Infantry Division. In October 1943 he became a military judge of the Martial Court at Polish First Army. In 1945 he was promoted to a judge of Supreme Court Martial. In the Court, Muszkat was a vice-chairman and chief of the War Crimes Commission. After his return to Poland with the Soviet westward offensive in 1945, he became a member of Polish Workers' Party. On 5 December 1946 Muszkat was demobilized from army as a colonel.
After the war he began his work in the Stalinist Ministry of Justice as deputy in the Polish Highest Military Court, investigating German war crimes. Muszkat was a specialist in the field of international public law, therefore the Ministry of Justice dispatched him to Nuremberg, as chairperson of the Polish delegation. At the Nuremberg Trials Mushkat directed Polish delegation which also included Prof Tadeusz Cyprian and prosecutors: Prof Jerzy Sawicki and Dr Stanisław Piotrowski. They prepared “Polish indictment” containing the list of proved Nazi war crimes committed in Polish territory. Having returned to Poland he began scientific and didactic activity. At University of Warsaw he lectured military law and international public law in International Public and Private Law Department, directed by prof Cezary Berezowski. He also lectured at Central Law School, General Headquarters Academy and Polish International Affairs Institute. In 1950, for his dissertation in the Stalinist International criminal law, new domain development he was awarded a professorship. He was co-founder and editor Law and Life magazine. Mushkat wrote from the pro-Soviet point of view. He propagated communist ideals, especially those of his mentor Andriej Wyszynski. Amongst Polish scientist Muszkat has some opponents. For instance prof. Stefan Korboński wrote later that "Muszkat's views transformed the courts into a political institution, with prosecutors as masters of life and death of absolutely everyone and barristers, as communist police helpers."