Shakhnovich was born in 1918 in Starokonstantinov, Ukraine to the family of a Jewish worker. He studied at a Yiddish school in his town, then worked at the Starokonstantinov sugar mill as a heating technician. He was drafted in 1938; in 1941 Shakhnovich graduated from the Baku Military school as a lieutenant. He saw action from November 1941 as the commander of an artillery battery of the 91st Rifle Division on the Southern Front. In 1942 he took part in the Stalingrad operation.
When the German Army entered the town of Starokonstantinov in July 1941, Shakhnovich's parents and his siblings were killed by Ukrainian collaborators.
Shakhnovich was awarded the title of Hero of the Soviet Union (as well as the Order of Lenin) after the fighting for the city of Melitopol, southern Ukraine in October 1943. Captain Shakhnovich and his battery were engaged in street fighting in the central part of the city; they managed to reconquer five city blocks, but Shakhnovich was wounded. After his release from a hospital, he continued fighting in eastern Ukraine, in Crimea and, later, in the Baltics. In addition to the title of Hero of the Soviet Union and the Order of Lenin, he was also awarded the Order of Red Star and several medals.
After the war, Moisei Shakhnovich settled in Baku, Azerbaijan, where he had studied at military school. In this city, he became the manager of a food shop. In the 1950s, when the delivery of some foodstuffs was limited, he supplied the local synagogue with flour for baking matzoth. In 1956, a new district attorney came to his shop and right out said to Shakhnovich that a Jew could not be a manager of such a shop. Being strong, Shakhnovich threw the attorney out of the shop. As a result, he was sentenced to a five-year prison term. However, due to his status as a war hero, his wife Esther and fellow war veterans of his managed to secure his release, but only after more than a year in prison.
Shakhnovich died in 1982. As a Hero of the Soviet Union, he had the right to be buried on the Alley of Honor in Baku but, according to his last will, he was buried in the local Jewish cemetery.