According to the Buffalo News, it's expected Tropp will miss 5-6 weeks.
Tropp was injured during a preseason game Sunday against the Toronto Maple Leafs.
Rolston also revealed that Tropp suffered a concussion against the Maple Leafs, but that it wasn't as much of a concern as the broken jaw.
"He is already cleared there, so I think that's not the concern right now," Rolston said of the concussion. "It's just getting him back healthy and keeping his weight on."
It's the latest injury for Tropp, who sat out the entire 2012-13 NHL season due to a knee injury sustained while playing in the American Hockey League season during the lockout.
Two seasons ago, Tropp debuted with the Sabres and had three goals and eight points in 34 games.