The Purple Rain singer was found unresponsive in an elevator at his compound in Paisley Park, Minnesota on Thursday morning (local time).
His cause of death wasn't immediately clear.
Carver County Sheriff Jim Olson says first responders tried CPR but couldn't revive the musician, who was pronounced dead at the scene at 10.07am local time (3.07am NZ time), about half an hour after police arrived.
Police were investigating his death, which followed the postponement of several recent concerts.
Fans quickly gathered outside his music studio following confirmation of his death.
The road near Paisley Park was closed, amid gridlock as a stream of mourners made their way towards the compound, where they laid purple flowers.
News of his death was accompanied by speculation he knew his time was running out, after the star recently revealed he had begun writing his memoir.
Prince performed in New Zealand for the very first time in February this year, with two Auckland shows quickly selling out.
He had more recently battled ill health that forced him to cancel performances.
On April 15, he suffered a medical emergency that forced his private plane to make an emergency landing in Illinois. He was taken to hospital for about three hours of treatment, before being released.
He performed a show the following day to reassure fans about his health.
"Wait a few days before you waste any prayers," Prince reportedly told fans at the show.
His representatives told TMZ that Prince had been battling the flu, while a source told the Minnesota Star Tribune that Prince had been suffering dehydration.
Prince last month announced during a New York performance that he would release a memoir, titled The Beautiful Ones, in early 2017.
Publishing house Spiegel & Grau was yet to comment on Prince's death. A press release about the memoir said: "Prince will take readers on an unconventional and poetic journey through his life and creative work."
It said the book would include stories about Prince's music and "the family that shaped him and the people, places, and ideas that fired his creative imagination."
A STAR IS BORN
The Minneapolis native stood just 157 centimetres in height, and seemed to summon the most original and compelling sounds at will, whether playing guitar in a flamboyant style that openly drew upon Jimi Hendrix, switching his vocals from a nasally scream to an erotic falsetto or turning out album after album of stunningly original material.
He shot to fame in 1982 after the huge success of his breakthrough album, 1999.
Among his other notable releases: Sign O' the Times, Graffiti Bridge and The Black Album.
He scored a string of hits, including Purple Rain, Little Red Corvette, and The Most Beautiful Girl in the World, selling over 100 million records during his career, and picking up seven Grammy Awards.
He also won the Academy Award for Best Original Song Score for Purple Rain in 1985.
Rarely lacking in confidence, Prince effortlessly absorbed the music of others and made it sound like his own, whether the James Brown guitar riff on Kiss or the Beatle-esque, psychedelic pop of Raspberry Beret.
He also proved a source of hits for others, from Sinead O'Connor's Nothing Compares 2 U to Cyndi Lauper's When You Were Mine. He also wrote Manic Monday for the Bangles.
Prince was fiercely protective of his independence, battling his record company over control of his material and even his name.
Prince once wrote "slave" on his face in protest of not owning his work and famously battled and then departed his label, Warner Bros., before returning a few years ago.
"What's happening now is the position that I've always wanted to be in," Prince told The Associated Press in 2014. "I was just trying to get here."
In 2004, Prince was inducted into the Rock and Roll of Fame, which hailed him as a musical and social trailblazer.
"He rewrote the rulebook, forging a synthesis of black funk and white rock that served as a blueprint for cutting-edge music in the Eighties," reads the Hall's dedication.
"Prince made dance music that rocked and rock music that had a bristling, funky backbone. From the beginning, Prince and his music were androgynous, sly, sexy and provocative."
Throughout his career, Prince was romantically linked to many female and male stars, including Madonna, Kim Basinger, Carmen Electra and Boy George.
He married Mayte Garcia, a back-up dancer in 1996. The couple broke up in 2000, and Prince married Manuela Testolini the following year, before divorcing in in 2006.
Prince had been touring and recording right up until his death, releasing four albums in the last 18 months, including two on the Tidal streaming service last year.
He performed in Atlanta last week as part of his Piano and a Microphone tour, a stripped down show that has featured a mix of his hits like Purple Rain or Little Red Corvette and some B-sides from his extensive library.
Prince debuted the intimate format at his Paisley Park studios in January, treating fans to a performance that was personal and was both playful and emotional at times.
The musician had seemed to be shedding his reclusive reputation. He hosted several late-night jam sessions where he serenaded Madonna, celebrated the Minnesota Lynx's WNBA championship and showcased his latest protege, singer Judith Hill.