Mironov studied in the Vakhtangov Theatre School during the early 1950s. From 1958-1962 he studied acting at the Moscow Shchukin School. From 18 June 1962-1987 Mironov was a permanent member of the trope at the Moscow Theatre of Satire. In 1962, he acted in his first film, What If This Is Love? On 18 December 1980 he was awarded the title of People's Artist of the RSFSR.
Andrei Mironov is known and loved for his roles in films made by Eldar Ryazanov, Leonid Gaidai, Mark Zakharov, and other directors. He had a wide comedic range and played diverse roles (e.g. a Soviet bureaucrat, Figaro, a romantic spy, a member of the Russian intelligentsia, a con man, an American movie pioneer, a tale-teller, etc.).
On one of his tours through Latvia in 1987, he lost consciousness while performing the lead role in The Marriage of Figaro. He was driven to a hospital where two days later he was pronounced dead on August 16, only nine days after the passing of his close friend and frequent co-star Anatoli Papanov. The cause of his death was excessive internal bleeding due a bursting of a congenital cerebral aneurysm.