A cause of death was not immediately available, and President Nelson said he doesn't expect to know "for a couple of days."
Born to jazz musician John L. Nelson and Mattie Della Shaw in 1960, two years after Prince, Nelson was a singer-songwriter, releasing four albums across her career, starting with 1988's "Royal Blue." That album produced her biggest hits, "Marc Anthony's Tune," which spent 11 weeks on Billboard's Hot R&B/Hip-Hop Songs chart, peaking at No. 33, and "L.O.V.E.," which spent seven weeks on the chart and topped at No. 52.
At the time, she told the Star Tribune of Minneapolis, "The album is basically about love relationships between a man and a woman. I'm royal blue because I can't find him," she said.
It's an alternative to her brother's chosen color of purple. Of their relationship, she said: "The funniest thing is people say, 'How does it feel to be Prince's sister?' They don't actually realize what they're saying. I've been Prince's sister ever since I got here on Earth."
The Associated Press described her "Royal Blue" album as "mostly adult-contemporary or easy-listening" material, "far removed from Prince and the so-called Minneapolis sound. Hers is a mature, romantic sound aimed at 25- to 45-year-olds."
Then came 1992's "Yellow Moon, Red Sky," 2008's "A Brand New Me," and finally, 2011's "Hustler."
Nelson is survived by two sons, President and Sir, and five grandchildren.
"Born 1960, the daughter of Mattie and John Nelson, she was best known as Prince's sister and worked to keep his legacy alive with his fans attending fan and industry events," President Nelson shared in a statement. "Services will be private, and in lieu of flowers, the family has asked that you take care of one another."
According to the Star Tribune, Nelson was scheduled to retire and perform a farewell concert at the Dakota in downtown Minneapolis in June. Illness caused her not to take the stage. A few days before the concert, she said she had a mixtape on the way and was working on a memoir.
Prince died of an accidental fentanyl overdose in 2016 at his home in Minneapolis. He was 57. He had no will, and his six siblings inherited equal interests in the estate: Tyka Nelson and five half-siblings -- Sharon Nelson, Norrine Nelson, John R. Nelson, Omarr Baker and Alfred Jackson.
Tyka Nelson, Baker and Jackson, the three youngest, sold their stake to a music publishing company called Primary Wave Music, LLC, which later assigned its interests to an affiliate, Prince OAT Holdings LLC. Jackson has since died.
Representatives for Paisley Park, Prince's private estate which is also a museum, studio, and concert venue in Chanhassen, Minnesota, did not immediately respond to The Associated Press' request for comment.
