The Los Angeles Times reported that Avildsen's eldest son said the director had pancreatic cancer.
Avildsen came up the hard way in films, starting with a long apprenticeship as assistant director, then moved up to production manager, cinematographer and editor.
Avildsen's other films included the critically hailed drama-thriller "Joe" (1970), starring Susan Sarandon and Peter Boyle. That film also impressed Frank Capra, who was incidentally Avildsen's favourite director.
A friend sent Avildsen the "Rocky" script.
He had been hired to direct Saturday Night Fever after his success with Rocky, but was let go amid differences over his desire to make the story more upbeat than the producers had in mind.
Stallone took to Instagram to pay tribute to Mr Avildsen, who helped usher the actor to stardom: "R. I. P". When he was offered the director's chair for Rocky Part II, though, Avildsen turned it down; he later called that decision "one of my greatest mistakes".
What's your favorite John G. Avildsen film? He received an Oscar nomination in 1983 for his documentary short film Traveling Hopefully.
After "Joe", Avildsen directed "Save the Tiger" (1973) starring Jack Lemmon as a burned-out dress manufacturer. Any filmmaker telling a tale of an underdog who gets their shot, or even just a story of personal redemption, or heck, a a movie in which people play sports, has watched Rocky and paid close attention. Sylvestor Stallone, Ralph Macchio, Martin Scorsese and other Hollywood actors and directors provide interviews about Avildsen's incredible directing abilities - it's definitely worth checking out this weekend.
He is survived by three sons Anthony, Jonathan and Ashley and a daughter, Bridget.