He died at his home in Manhattan. His stepdaughter, Leslie Gimbel, told the newspaper that the director was battling lymphoma.
Lumet's films included "12 Angry Men", "Network" and "Dog Day Afternoon."
Lumet was nominated for Academy Awards four times as a director. He never won, but he did receive an honorary lifetime achievement Oscar in 2005.
The Associated Press and City News Service contributed to this report.