The goalie made 21 saves in a 3-2 overtime win against the Edmonton Oilers on Monday. He appeared to be in discomfort in the second period but remained in the game.
"It was not one specific play," Canadiens coach Dominique Ducharme said Tuesday. "It's something that has been carrying on for a little bit of time. We just want to make sure he can take care of it and come back being 100 percent."
Price will remain in Montreal for treatment but has not been ruled out when the Canadiens host the Winnipeg Jets on Thursday.
"The info we have is it's not something that is dangerous for his season or career," Ducharme said. "We're going to know more … in a couple days. … The chances of Carey playing against Winnipeg, it's hard to tell right now because we need to see how he reacts after a couple days. But yeah, there's a chance that Jake [Allen] will play both games."
Price is 12-6-5 with a 2.66 goals-against average, .903 save percentage and one shutout in 23 games this season.
Allen will start against the Maple Leafs. He is 5-3-4 with a 2.23 GAA and .922 save percentage in 12 games.
"Nothing changes for me," Allen said. "Carey, he's done a great job for us and now I get a chance to go in there and play a couple of games and have some fun with it. I'm preparing the same way as I would whether I'm playing or not playing. It really doesn't change for me. ... I'm looking forward to getting back in there tomorrow against a good team. I haven't faced Toronto yet, so it'll be fun."
Cayden Primeau was recalled from Laval of the American Hockey League and placed on the taxi squad. He will back up Allen on Tuesday.
Montreal forward Brendan Gallagher is out indefinitely after the forward broke his right thumb in the first period Monday. He left at 13:28 of after he was hit by a shot by teammate Alexander Romanov.
"He's the engine. He really is," Allen said of Gallagher. "You know what you're getting from 'Gally' every game. He's going to be in the hard areas. He's going to do the things that you know you need to do and pay the price to win. And don't get me wrong, those are really tough shoes to fill, but I think we have a lot of guys in this room that can really fill that."
Gallagher scored 23 points (14 goals, nine assists) in 35 games this season.
"It's tough. He's a warrior in front of the net, and these kinds of things might happen through the season," Montreal forward Tomas Tatar said Monday. "Obviously, he will be missed, and we have to do everything we can and battle and get as many points until he gets back, and hopefully he will be ready to play for us."
Jesperi Kotkaniemi will take Gallagher's place at right wing on a line with center Phillip Danault and left wing Tomas Tatar against the Maple Leafs.
NHL.com columnist Dave Stubbs and independent correspondent Sean Farrell contributed to this report
