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 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.
"Devane's a big guy, 6-foot-5," Rolston said after Sunday's game. "And [Tropp's] a smaller guy, but certainly a battler. So guys weren't happy about it."
Tropp was left bloodied on the ice after the fight and had to leave the game.
"[Tropp] was the guy who instigated the fight," Leafs coach Randy Carlyle said when asked about the incident that allegedly spurred Scott to go after Kessel.
"Obviously, maybe they felt that was the problem was that there was a bigger man fighting a smaller guy."
Information from The Associated Press was used in this report.