The goalie had an MRI on Monday after he was injured in the first period of a 5-1 loss to the Boston Bruins on Jan. 12.
The update on Allen came after the Canadiens on Monday said goalie Carey Price, who has not played this season, would have to restart rehabilitation on his surgically repaired knee.
Sam Montembeault (16 games this season) and Cayden Primeau (four) are the goalies on Montreal's active roster.
Montembeault has started six of the past eight games. He made 48 saves in a 5-3 win at the Dallas Stars on Tuesday and made 49 saves in a 4-3 overtime loss at the Vegas Golden Knights on Thursday.
"I've had a lot of work, but at the same time that really allows me to stay in the game and not have a lot of down time," Montembeault said. "I feel really good when I'm playing and that's going well. And the important thing about playing a lot is being consistent and giving my best effort every game."
The 25-year-old is 2-6-4 with a 3.73 goals-against average and .904 save percentage this season.
"I think he's made nice progress since he's been here, but he still has things to work on, which he is doing with (goaltending coach) Eric [Raymond]," Montreal coach Dominique Ducharme said. "We see gradually that it's coming together, a bit like a puzzle, and he's more and more comfortable and it's paying off for him and us too."
Primeau is expected to start Saturday at the Colorado Avalanche, who lead the NHL in scoring (4.18 goals per game).
"It's a big challenge for him and for our team," Ducharme said. "They're an excellent team. When you look around the NHL, they're certainly one of the best teams and they are hard to beat at home (16-2-1). So it's going to be a challenge for everyone."
The 22-year-old played 16 games for Laval of the American Hockey League this season and has played two NHL games since Dec. 16, including two periods against the Arizona Coyotes in a 5-2 loss Monday.
"Obviously playing a lot at the beginning of the year was good," Primeau said. "I haven't played over the last month and a half, but I'm excited that I was able to get into a game a couple of days ago and getting another start again. Just being able to practice with these guys and face these shots, it's huge."
Ducharme was asked if it would be better to have Primeau playing more in the AHL.
"For sure this situation leaves us no choice. So he'll be in goal tomorrow," he said. "He's had a few days to practice. With the COVID he had before he played in Arizona, we tried to give him as many reps as we could, but that wasn't a lot. So he's had a few more days now. The important thing is that he experiences every moment. In a perfect world, with everyone healthy, playing him as often as possible would be most important. But we don't have that luxury right now."
Michael McNiven was recalled from Laval to the taxi squad on Jan. 13.
Allen was 5-16-2 with a 3.15 GAA and .901 save percentage in 24 starts for the Canadiens (8-25-6), who are last in the NHL standings one season after losing the Stanley Cup Final to the Tampa Bay Lightning.
"It's been a long time since I've been a No. 1, probably in junior, because even in the AHL it's more about alternating starts," Montembeault said. "I'm happy, and it's a great challenge, and it's the first time since the start of my career that I've really had a chance to play several consecutive games in the NHL. So I'm eager to have this chance and seize this opportunity."
NHL.com independent correspondent Sean Farrell contributed to this report
