Price skated during Tuesday's practice but said he would not be ready to return for Wednesday's game against the Anaheim Ducks.
Peter Budaj is expected to make his fifth consecutive start for the Canadiens (34-22-7), who entered Wednesday with the third-best record in the Eastern Conference.
Price, who helped lead Canada to its second consecutive Olympic gold medal last month, told reporters that he aggravated a lingering injury during his second practice in Sochi. He played well despite the injury, posting shutouts in Canada's semifinal win over the United States and in the gold medal win over Sweden.
After receiving treatment from the Canadiens' medical staff Tuesday, Price worked briefly on the ice at practice.
"It felt good to get on the ice," Price told the team's official website. "It's coming down to the important part of the year, and I want to go into this stretch 100 percent."
The Canadiens placed Price on injured reserve Monday, but the three-time All-Star is considered day to day.
"I want to make sure I'm prepared for the rest of the year and the playoffs," said Price, who is 26-17-5 with a 2.33 goals-against average and a .925 save percentage this season. "We still have a lot of hockey left this year, and I want to make sure I'm good to go.
"[The injury is] manageable, but I want it to be 100 percent before we go into the important stages of the year."