Moisey Markov graduated from the Faculty of Physics of Moscow University in 1930.
Moisey Markov worked at the Institute of Red Professors (1931-1933) and the Faculty of Physics of the Moscow State University (1933-1934). Since 1934 he worked for the Lebedev Physical Institute. In 1956-1962 he was the head of the Neutrino Physics Laboratory of the Institute for Nuclear Research. In 1968-1988 he was the Secretary of the Department for Nuclear Physics of the Soviet Academy of Sciences.
Markov was a full member of the Soviet Academy of Sciences since 1966 (a corresponding member since 1953).