Patrick Cousins, Prince's general counsel, said Wednesday the case was pending. He had no further comment.
An attorney for Nelson did not return a telephone call from The Associated Press.
The Star Tribune reported on its Web editions Wednesday that the case was filed May 24. A court administrator told the AP the case was sealed on July 11.
Prince, 48, has rarely spoken publicly about his marriage to Nelson. He married dancer Mayte Garcia in 1996; that union ended in 1998.
The Minneapolis-based singer was inducted into the Rock and Roll Hall of Fame in 2004. He recently closed his NPG Music Club Web site, surprising many fans.