Menez was playing his first game for the club in a friendly against FC Lorient when Lorient midfielder Didier N'Dong accidentally trod on the right side of Menez's head, causing a part of the player's ear to be ripped off.
Bordeaux confirmed that the Frenchman underwent surgery and wished him a quick recovery.
"Jeremy was operated on under local anaesthesia on Wednesday night to sew up his ear," a club statement said.
"We wish a speedy recovery to our player and hope to see him back soon".