Mikhail Mikhailovich Kozakov was born on 14 October, 1934 in Leningrad, into the family of the writer Mikhail Emmanuelovich Kozakov and Zoya Aleksandrovna Nikitina, the editor of “Leningrad Writers’ Publishing House.”
During the war, Misha, along with other children in Leningrad, was evacuated to Molotovskaya oblast (now the border regions of Perm). From 1941 to 1944, he lived in the woods in Chernaya-Krasnokamskiy region. From 1945, he studied in the Leningrad Choreography College.
On graduating the 222nd Boys’ School in 1952, Mikhail Kozakov applied to MXAT. While in his final year of study, he made a successful film debut in the role of Charles Thibault in M.I. Romm's political drama, “Murder on Dante Street.”
In 1956, he graduated from MXAT and applied to work at the Mayakovsky Theatre, where he worked from 1956 to 1959. After that, he worked at the Sovremennik (1959-1970), at MXAT (1971-1972), in the Theatre on Malaya Bronnaya (1972-1981), and in the Lenkom Theatre (from 1986 onwards).