US media reported that Craven died at his Los Angeles home on Sunday from brain cancer.
Craven wrote and directed A Nightmare on Elm Street in 1984. His Scream franchise was reported to have grossed more than $100m (£65m) in the US.
He wrote, directed and edited his first film, The Last House on the Left, in 1972.
A tweet from his Twitter account featured a picture of him with the dates 1939-2015.