The cause of his death is still unknown and the results of April 22 autopsy could take at least four weeks.
Prince Nelson Rogers, 57, was found dead in a lift on his Paisley Park estate, near Minneapolis, on April 21, where fans are still paying tributes.
According to officials, there was no sign of trauma on the body and no indication the death was suicide.
Anna Meacham said Prince’s “final storage” would be kept private.
“A few hours ago, Prince was celebrated by a small group of his most beloved: family, friends and his musicians, in a private, beautiful ceremony to say a loving goodbye,” she said.
Among the people who attended the ceremony were percussionist Sheila E, bassist Larry Graham and Prince’s sister Tyka Nelson.
Prince was a Jehovah’s Witness which requires funerals to take place within a week of a person’s death.
His innovative music spanned rock, funk and jazz. He was at his peak in the 1980s with albums like Dirty Mind, 1999 and Sign O’ The Times. He sold more than 100 million records.
Prince was last seen at about 20:00 on April 20 and was found unconscious by some of his staff at about 09:30 the next morning.
He had been rushed to hospital in Illinois six days earlier, while flying home from a concert in Atlanta, Georgia, but was treated and released a few hours later.
Quoting unnamed sources, TMZ reported that Prince was treated in Illinois for an overdose of Percocet.
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