Leslie Gimbel, Lumet's stepdaughter, told The New York Times he suffered from lymphoma.
Lumet was born in Philadelphia in 1924 but came to New York, where he would set many of his best-known films, as a baby. His father acted in the Yiddish theater and the son made his debut at 4 and appeared on Broadway at 11 in the play "Dead End."
He started directing off-Broadway and for television, where his work included a version of "12 Angry Men," which he remade for the big screen in 1957 as his first feature film. He went on to make a string of critical and box office successes, including "Serpico," "Prince of the City," "Dog Day Afternoon," all fact-based movies set in New York, and "The Verdict."
"While the goal of all movies is to entertain, the kind of film in which I believe goes one step further," Lumet said. "It compels the spectator to examine one facet or another of his own conscience. It stimulates thought and sets the mental juices flowing."
Lumet's last movie, "Before the Devil Knows You're Dead," was released in 2007 when he was 83.
He was nominated four times as a director for Academy Awards. In 2005 he was awarded a special Oscar for lifetime achievement.