Smyth played only two shifts in the first period before suffering the injury. He was wearing a cast after the game, but the team said surgery likely won't be required.
"I couldn't move my thumb," Smyth said after the game. "I had no movement at all. I thought maybe it was dislocated or something.
"I hated to leave. You want to be out there contributing."
The 30-year-old leads the Oilers with 16 goals in 25 games this season. His absence comes on the heels of the Oilers losing third-leading scorer Ales Hemsky to a shoulder injury. Hemsky, who was hurt in Edmonton's loss to Anaheim on Nov. 28, is expected to miss another week or two.