Fyodor Dunayevsky was born in Moscow. His great-grandfather was an architect. His grandfather was a professor of history. His father was a biophysicist. His parents divorced when Fyodor was fourteen years old. He studied at School No. 875, where he took part in a theater studio. He was expelled from school several times, and after another fight he was placed on record with the juvenile affairs inspectorate. At the age of fourteen he worked as a janitor at a kindergarten. He studied at a medical college, after graduating from which he worked as an emergency medical technician. He was interested in chess and biathlon. He got into cinema by chance. His classmate Anastasiya Nemolyaeva took photographs of several of her classmates to auditions at Mosfilm in the acting department. Fyodor was invited to audition and was then offered the lead role in the film Courier (1986) by Karen Shakhnazarov. During Arnold Schwarzenegger and Tom Cruise's visit to Moscow, Fyodor Dunayevsky was their guide around Mosfilm. In 1991 he repatriated to Israel and performed at the Tel Aviv Cameri Theater.

He worked in radio and voiced TV series. He appeared in the series Tel Aviv Youth. He worked as a model for designer Doron Ashkenazi (Tel Aviv, Israel). In 1993-1995 he returned to Moscow and studied in the directing department of VGIK (Sergei Solovyov and V. Rubinchik's workshop). In 1996-2000 he lived in Italy. He organized a company specializing in freight transportation. He opened its branches in Kazakhstan and Ukraine. After closing the business in 2001, he opened the production center Kalitka. He returned to Russia several times and appeared in TV series. In 2016-2017 he was involved in music, creating the group Banda Dunaevsky. In it Fyodor was the vocalist, and the musicians were Valentin Petrichenko's Burlesque Orchestra. The group performed a repertoire in Italian - Blue Canary, Tu vuò fa l'americano, Criminal Tango, Quando Quando Quando and other songs. In 2017 Dunayevsky played the role of a bank clerk in the music video for the group SerGa, Primety.