The sister, Tyka Nelson, asked in documents filed in a state court in Carver County, Minnesota that a special administrator be appointed to handle his affairs and that she be appointed to probate the singer and musician's estate.
She listed herself and five other siblings or half-siblings as Prince's heirs but gave no value of his assets or debts. Prince, born Prince Rogers Nelson, was married and divorced twice and had a son who died shortly after birth in 1996.
The value of his existing music catalogue alone has been estimated at over US$500 million (NZ$745 million), according to the musician's first manager, Owen Husney. That included potential licensing rights to film, TV, commercials and videogames that Prince rarely exploited, Husney said in an interview last week.
The eclectic, influential songwriter and performer behind hits like "Purple Rain" was found dead on Thursday (Friday NZT) at age 57 in an elevator at his Paisley Park Studios compound in Chanhassen, a Minneapolis suburb. The cause of death was not yet known.
In her petition for the appointment of a special administrator, Nelson said, "I do not know of the existence of a will and have no reason to believe that the Decedent executed testamentary documents in any form."
She added that an administrator was needed "because no personal representative has been appointed in Minnesota or elsewhere." Nelson proposed the Bremer Bank in Minnesota for the administrator role, saying it had done business for years with Prince, a Minneapolis native.
Prince's remains were cremated and on Saturday he was given a private family ceremony.
Since his death, sales of his albums have soared, with more than 2.3 million songs and some 580,000 albums sold since Thursday, according to Nielsen Music, taking Prince to the top of the Billboard album charts.
Aside from royalties from his more than 30 albums, Prince regained ownership of his master recordings after a well-documented dispute with his Warner Bros. music label.
He was also said to have a cache of unheard recordings, including an album recorded with the late jazz trumpet great Miles Davis.
Minnesota-based attorney Stephen Hopkins said it was unusual for a person of Prince's stature and wealth to die without a will. In such cases, assets are split evenly between the heirs, Hopkins said.
"This (case) is going to be open for some time, probably for some years," Hopkins, of the Minneapolis firm Henson & Efron, said in an interview.
He said the administrator's first job would be to ascertain all of Prince's assets, paying any debts he owed and paying taxes.