The singer and musician's influential, genre-defying music combined jazz, funk, R&B and disco, winning seven Grammy awards and an Oscar.
Prince was found unresponsive in an elevator at his Paisley Park Studios compound, which included his home, in the Minneapolis suburb of Chanhassen, according to a Carver County Sheriff's Office statement. Emergency workers tried to revive him and he was pronounced dead a short time later.
The sheriff's office said it was investigating the circumstances. The local medical examiner declined to comment on the cause of death.
President Barack Obama paid tribute to Prince as a "one of the most gifted and prolific musicians of our time."
"Few artists have influenced the sound and trajectory of popular music more distinctly," Obama said in a statement. "Prince did it all. Funk. R&B. Rock and roll. He was a virtuoso instrumentalist, a brilliant bandleader, and an electrifying performer."
Distraught devotees gathered with media crews outside the Paisley Park compound to mourn the artist.
"His music made the hair on your arms stand up," said one fan, Kristina Dudziak, 44. "It felt like he was making love to his guitar. ... It's a sad day," she added, starting to sob.
Sheila E., a singer and percussionist who worked closely with Prince in the 1980s, wrote on Twitter: "My heart is broken. There are no words. I love you!"
Prince's death, first reported by celebrity website TMZ, was the most notable passing of a music giant since David Bowie died of cancer at 60 on Jan. 10.
Prince, whose hit songs also included "Raspberry Beret," "Little Red Corvette" and "Kiss," was on a U.S. tour as recently as last week.
Last Friday, he was briefly hospitalized with the flu after his plane made an emergency landing in Moline, Illinois, TMZ reported. A representative said Prince had performed in Atlanta even though he was not feeling well and felt worse after boarding the plane for a flight back to Minnesota, according to the website.
Prince first found fame in the late 1970s. Over the next three decades, he became known as one of the most inventive and eccentric forces in American pop music.
Often making a statement with bold fashion choices, the diminutive, 5-feet 2-inch-tall (1.57-meter) star sometimes appeared on stage sporting ruffled shirts and tight pants or elaborate costumes, including chain mail covering his face, a shimmery orange tunic with a cane, or bikini briefs.
He was regarded as a perfectionist who from 1993 to 2000 changed his name to an unpronounceable symbol in what was seen as a protest against his record label at the time. For a while, he was dubbed "The Artist Formerly Known as Prince."
An intensely private person, Prince sold more than 100 million records. In addition to his seven Grammy awards, he was inducted into the Rock and Roll Hall of Fame in 2004. His most recent album, "HITnRUN: Phase Two" was released in December 2015.
Prince became a Jehovah's Witness about 15 years ago, and was a strict vegan. In 2009, he spoke in a PBS television interview about being born an epileptic and suffering seizures as a child.
He said he was also teased in school, and that "early in my career I tried to compensate by being as flashy as I could and as noisy as I could."
Prince's Oscar was for best original song score for "Purple Rain," the 1984 movie whose music was based on his album of the same name. He also starred in the movie.
In 2007, he played the Super Bowl in one of the most celebrated such performances.
While he was more accustomed to performing in arenas, two years ago Prince played perhaps his most intimate gig in the living room of British singer-songwriter Lianne La Havas' London home with his band, 3rdeyegirl, Billboard said.
"We'll work our way up, if people like us, to bigger venues," Prince quipped then.
Born in Minneapolis as Prince Rogers Nelson on June 7, 1958, he is said to have written his first song at age 7. As well as singing and writing, he played multiple instruments, including guitar, keyboards and drums.
His music was marked by sexually charged lyrics and explosive live performances, while his private life was marked by a string of romances linking him with the likes of Madonna and actresses Kim Basinger and Carmen Electra.
Prince was married twice: to his backup singer, Mayte Garcia, in 1996 and then to Manuela Testolini in 2001. Both marriages ended in divorce, and a son he had with Garcia died a week after birth in October 1996.
Describing him as a "once-in-a-lifetime artist," music TV channel MTV said it was changing its logo to purple for the day in honor of Prince. Twitter lit up with reaction from dismayed friends and fans.
In a 1998 interview with Reuters' Franklin Paul, Prince chuckled as he said he ignored the critics and that he had no expectations for his then-current album. Expectations take away from the quest for great music, he said.
"I don't expect anything," Prince said. "I just do what I feel I'm supposed to do."