Levy was born to a Jewish family in downtown Hamilton, Ontario. His mother, Rebecca (née Kudlatz; 1910–1988), was a homemaker, and his father, Joseph (1909–1985), was a foreman at a car factory. He has a brother, Fred, and sister, Barbara. His mother was born in the Gorbals area of Glasgow, Scotland, to Polish Jewish parents, and later moved to Canada. His father was Sephardi Jewish, with ancestors from Spain and Bulgaria.
Levy attended Westdale Secondary School, where he was student council president. He faced antisemitic bullying, with his campaign posters defaced with the word "Jew", which he refused to take down. He subsequently attended McMaster University, graduating in 1969 with a Bachelor of Arts in sociology. He was vice-president of the McMaster Film Board, a student film group, where he met filmmaker Ivan Reitman.
