The injury occurred when Russell pushed forward on a 4-yard run with 5:36 left in the fourth quarter. Postgame X-rays and a CT scan revealed the fracture. He will see a specialist Monday.
Baylor coach Art Briles told ESPN's Brett McMurphy that Russell would "probably be out awhile" but won't "find out for certain until Monday."
"He's a tough guy. It's hard to see tough guys hurt," Briles said.
Backup quarterback Jarrett Stidham took over on the Bears' next drive. He would get the start if Russell can't play for the second-ranked Bears, who have an off week before traveling to Kansas State for a Thursday night game Nov. 5.
"This is a tough deal for Seth," Briles said. "Stidham is the best young quarterback I've been around. He's very polished."
Coming into the weekend, Russell was leading the nation with 27 touchdown passes to just five interceptions. He added two touchdown throws and one pick Saturday. He threw for 197 yards on 16-of-37 passing.
The Associated Press contributed to this report.