Khitruk was born in Tver, Russian Empire and came to Moscow to study graphic design at the OGIS College for Applied Arts. He graduated in 1936 and started to work with Soyuzmultfilm in 1938 as an animator. From 1962 onwards, he worked as a director. His first film The Story of a Crime was an immense success. Today, this film is seen as the beginning of a renaissance of Soviet animation after a two-decade-long life in the shadows of Socialist realism.
Diverging from the “naturalistic” Disney-like canons that were reigning in the 1950-60s in Soviet animated cartoons, he created his own style, which was laconic yet multi-level, non-trivial and vivid.
He is the director of outstanding animated short films including such classics as his social satire of bureaucrats, Chelovek v ramke (The Man in the Frame) (1966), the philosophic parable, Ostrov (Island) (1973) about the loneliness of a man in modern society, the biographical film Ein Junger Mann namens Engels - Ein Portrait in Briefen (1970), based on drawings and letters of young Engels, the parody Film, film, film! (1968), and the anti-war film, Lev i byk (The Lion and the Bull) (1984).
During his long career, he was awarded innumerable awards by all major film festivals. Today, Fyodor Khitruk lives in Moscow.
In April 1993, Khitruk and three other leading animators (Yuriy Norshteyn, Andrey Khrzhanovsky, and Eduard Nazarov) founded SHAR Studio, an animation school and studio in Russia. The Russian Cinema Committee is among the share-holders in the studio.
In 2008, he released a two-volume book titled The Profession of Animation («Профессия – аниматор»). He is the grandfather of violin virtuoso Anastasia Khitruk.