Jason Francesco Schwartzman was born in Los Angeles on June 26, 1980, the son of actress Talia Shire (Coppola) and film producer Jack Schwartzman. His paternal grandparents were Polish Jews, while his mother is an Italian-American Catholic. His younger brother, Robert Schwartzman, is also an actor and musician. His paternal half-siblings are Stephanie and cinematographer John Schwartzman.

As a member of the Coppola family, many of his relatives are also involved in the entertainment industry—he is the nephew of filmmaker Francis Ford Coppola and opera conductor Anton Coppola; the cousin of actor Nicolas Cage and filmmakers Sofia Coppola, Roman Coppola, and Christopher Coppola; and the grandson of Coppola family matriarch Italia Coppola (Pennino) and composer Carmine Coppola. He attended Windward School in the Mar Vista neighborhood of Los Angeles.