Coach Ron Rolston said Wednesday that Tropp is expected to miss at least five weeks after having surgery to repair the jaw. Tropp also sustained a concussion.
Tropp's head was bloodied following a fight with Toronto's Jamie Devane midway through the third period of Buffalo's 5-3 loss on Sunday. A full line brawl occurred before the next faceoff, when Sabres enforcer John Scott went after Toronto's Phil Kessel.
The brawl led to 211 penalty minutes and three ejections.
Rolston was fined by the NHL, which deemed he was partially responsible for his player selection and team conduct.