His lawyer said the wrestler died at his son-in-law's home in Florida surrounded by family and friends.
The Fijian-born former wrestler had spent time in a hospice for several conditions including dementia, though it's not clear yet how he died.
In a statement on its website, the WWE said it was saddened to learn of his death and hailed him as "the pioneer of high-flying offense" in the ring.
His daughter Tamina Snuka, also a WWE star, tweeted "I love you dad" with a picture of the two.
It's less than two weeks since homicide charges were dropped against Jimmy Snuka relating to the death of his girlfriend in 1983.
A judge ruled that he was mentally incompetent to stand trial over the death of 23-year-old Nancy Argentino.
The charges were only brought in 2015.
He pleaded not guilty to third-degree murder and involuntary manslaughter.
Wrestling stars have been paying tribute to Snuka online