The Manchester-born star, who lived in Hollywood, Florida, was rushed to hospital suffering from a cardiac arrest, but could not be resuscitated.
His manager and brother-in-law, Joseph Pacheco, paid tribute, describing him as an “incredible human being”.
Jones found fame as the frontman of the Sixties group the Monkees, who had nine top 40 hits including I’m A Believer, Daydream Believer and Last Train To Clarksville.
A spokeswoman for the medical examiner’s office for Martin County, Florida, said: “The medical examiner’s office has been informed of the death of Mr Davy Jones. The medical examiner’s office will take jurisdiction and a possible autopsy will be performed and evaluation of the circumstances of death and medical information.”
Jones is survived by his third wife Jessica, his four daughters, Talia Jones, Sarah McFadden, Jessica Cramar and Annabel Jones – three sisters, Hazel Wilkinson, Beryl Leigh and Lynda Moore, and three grandchildren.
Mr Pacheco said: “All of his family, friends and fans mourn Davy’s loss.
‘“We were fortunate to have such an incredible human being in our lives.
“Sadly, his time on Earth was cut far too short and he will be missed tremendously by all who knew him.”
Jones, who was best known as the frontman of the band put together to star in their own television show, had an early start in showbusiness when he appeared as Ena Sharples’ grandson in Coronation Street.
He also appeared in Z Cars, before leaving showbusiness to train as a jockey but came back to the acting, playing the Artful Dodger on stage in Oliver!
He appeared in the West End and followed the show to Broadway, landing a Tony nomination, and built up a career as an actor and singer before he auditioned for the Monkees.
Despite a flurry of hits, the band were initially criticised for the manufactured nature of their career, with Californian rivals the Byrds mocking them in their single So You Want To Be A Rock ‘n’ Roll Star. But they eventually proved themselves, writing more of their own songs, playing live on tour, and later starring in 1960s cult film Head with Jack Nicholson.
In a statement Jones’s publicist, Helen Kensick, said he died near his passion – his horses – with his wife an hour away.