Canadiens coach Michel Therrien said Price aggravated the injury while representing Canada at the Sochi Olympics.
"He will not play the next two games and he's day-to-day," Therrien said.
The Canadiens host the Detroit Red Wings tonight. Peter Budaj will start in goal, and Dustin Tokarski has been called up from the AHL's Hamilton Bulldogs to serve as backup.
Therrien said that Price will not accompany the team on a trip to Pittsburgh for a game Thursday night and would be re-evaluated on Friday.
He was originally expected to make his return Saturday against the Maple Leafs in Toronto. His status for that game is unclear.
Price was participating in his first practice with the Canadiens since helping Canada win a gold medal in Sochi. He was injured while moving laterally to make a save during a five-on-0 power play drill.
Detroit coach Mike Babcock, who also coached Canada in Sochi, said he was unaware of Price being injured during the Games.
But Canada captain Sidney Crosby, speaking to reporters in Pittsburgh, said Price was ailing in Sochi and handled both the pressure of the starting job and his injury well.
"I think it was something that didn't just happen at the Olympics," said Crosby. "I think it's something he's been battling for a while."
Price played in all but one of Canada's Olympic games, including a 3-0 win over Sweden in the gold medal game.
Price has a 26-17-5 record, a .925 save percentage and a 2.33 goals-against average with Montreal this season.