Backup goaltender David Rittich came in for the closing moments, holding on for a 3-2 win.
While neither the nature of Smith's injury nor a timeline has been announced, a prolonged absence could be devastating to the Flames, with the team in the thick of the Western Conference playoff race.
Smith has arguably been the Flames' MVP this season. He held a 22-16-6 record alongside a .921 save percentage entering Sunday's game.
The Flames acquired Smith from the Arizona Coyotes last offseason.
Smith struggled with groin ailments through six campaigns with the Coyotes, as he missed 12 games last season and another 40 contests the previous year.
The 35-year-old was also sidelined for the final 10 games of the 2013-14 campaign. Arizona finished that season with 89 points, missing the playoffs by just two points.
In all, Smith has had a long history of groin injuries since 2012: