Mikhail Rabinovich was born in 1901 in the city of Brest-Litovsk, Belorussia. His father rented a brick workshop. In 1915, during World War I, his family, along with all the other Jews in Brest-Litovsk, was forcefully deported eastward by the command of the tsarist army. Eventually Mikhail settled in the city of Poltava, where worked as a salesman.
In 1919 Rabinovich volunteered to join the newly established Red Army. He was involved in fighting against the Ukrainian and Polish armies and in southern Russia against the White Russians under the command of Generals Denikin and Wrangel. In 1923 he graduated from military school in Poltava and became an officer. In 1928 Mikhail Rabinovich completed the Vystrel course for senior commanders of the Red Army. From 1930 to 1934 he was a chief of staff of a division and from 1934 to 1937 he commanded the tank forces of an army. In 1939 – 1940 Rabinovich participated in the Soviet-Finish war. During the interwar period he was awarded the Orders of Lenin and the Red Banner.
During the Soviet-German war Mikhail Rabinovich rose from the position of commander of tank forces of an army to commander of tank forces (from February 1943) of the North-Western Front. He was awarded the rank of major-general in the summer of 1942. In the spring of 1944 he became the head of the Red Army's department for arming and repairing tanks. Subsequently he served as head of the armored forces of the 2nd Belorussian Front. His contribution was crucial to lifting the siege of Leningrad. During the war he was awarded several orders, including the very prestigious Order of Kutuzov, 2nd class, reserved for commanders of the Red Army. In 1944 the article by Shmuel Persov "The History of the Four Orders [military honors] of General Rabinovich" was prepared for the Jewish Anti-Fascist Committee and sent to Jewish newspapers abroad.
After the war, from 1946 to 1948 Mikhail Rabinovich commanded the tank forces of the White Sea Military District and served as a deputy corps commander. He retired from the army in 1954.
Mikhail Rabinovich died in 1977 in Moscow.