Greater Manchester Police were called on Tuesday after reports that a woman had been assaulted at a house in Hale.
A police statement reads: “The woman received a small cut to her hand and does not require hospital treatment.
“A 44-year-old was arrested on suspicion of assault and has been bailed pending further enquiries.”
Butt, who made 387 appearances for the club between 1992 and 2004, was appointed as head of the academy in 2016.
The senior United team bowed out to Barcelona in the UEFA Champions League on Tuesday night.