A statement on behalf of his fiancee, Reverend Omarosa Manigault, said he passed away at the Cedars-Sinai Medical Centre after having a heart attack in July.
The former bodyguard, who turned to acting in his 30s, never fully recovered and has been in hospital for almost two months.
The statement said: "Manigault is grateful for all of your prayers and asks for privacy at this time. Celebrations of his life, both private and public, will be announced at a later date."
Earlier this year, Duncan had appeared in a video for Peta, the animal rights organisation, in which he spoke of how much better he felt since becoming a vegetarian three years earlier.
"I cleared out my refrigerator, about $5,000 worth of meat," he said. "I'm a lot healthier than I was when I was eating meat."
The 6ft 5in actor appeared in dozens of films, including Armageddon, Planet of the Apes and Kung Fu Panda.
He had a handful of minor roles before The Green Mile brought him an Academy Award nomination for best supporting actor.
The 1999 film, based on the Stephen King novel of the same name, starred Tom Hanks as a corrections officer at a prison in the 1930s. Duncan played John Coffey, a convicted murderer.
Born in Chicago in 1957, Duncan was raised by a single mother whose resistance to his playing football led to his deciding he wanted to become an actor.
But when his mother became ill he dropped out of college and worked as a ditch digger and bouncer to support her.
By his mid-20s he was in Los Angeles where he looked for acting parts and became a bodyguard for Will Smith, Jamie Foxx and other stars.
The murder of rapper Notorious B.I.G., who Duncan had been hired to protect before switching assignments, led him to quit his job and pursue acting full-time. Source