The Irish singer shot to worldwide fame in 1990 with her cover of Prince's song Nothing Compares 2 U, but has confessed she loathes the Purple Rain star.
She alleges they had a huge bust-up when they met, but she is keeping details of the dispute a secret until she writes her memoirs.
O'Connor tells Uncut magazine: "I loved his music, but I had absolutely no idea or expectation that that single would be such a big hit, not at all.
"Did I ever meet Prince? I did and... we didn't like each other. At all. Ha ha! I'm not going to go into it, but we detest each other... It got violent too, which is why I can't go into it, but it is a very funny story. I'll tell it when I'm an old lady and I write my book."