Stollsteimer, 25, told police that White punched him seven times in the face. Police said Stollsteimer's right eye was bruised and swollen, and he was bleeding from his nose. He was treated and released from a Detroit hospital.
Prosecutor Marcus Connor said his office is awaiting results of the police investigation before deciding whether charges should be filed.
White, 28, told police he struck Stollsteimer in self defense. Stollsteimer's manager, Rick Canny, said "this was not a fight, this was an attack."
White's Spokeswoman Alison Zero declined comment Monday. White is the lead vocalist, songwriter and guitar player for the White Stripes, a two-piece rock band based in Detroit.