With 7:34 remaining in regulation and the Coyotes leading 3-2, Smith favored his right leg and was in obvious discomfort after forward Derick Brassard fell on top of him following a scramble in front of the net.
"He's being evaluated now. We'll see," Coyotes coach Dave Tippett said. "It's early. We don't know anything about it yet."
Making his 12th straight start, Smith has been a stalwart in Phoenix's quest to qualify for the Stanley Cup Playoffs. Entering the game Monday, Smith had a 27-21-10 record with a 2.65 goals-against average and .915 save percentage in 61 games.
Thomas Greiss finished the game for the Coyotes, who lost 4-3 in overtime. The backup goaltender was already scheduled to start Tuesday night on the road against the Pittsburgh Penguins. Any update on Smith's injury will provide more insight into exactly how long Greiss assumes that starting role.
"He was expected to play tomorrow anyway. That won't change," Tippett said.