Price, 25, just returned to the team Monday after helping lead Canada to gold at the Sochi Olympics.
Coach Michel Therrien said after practice that Price had aggravated a lower-body injury during the Winter Games and will miss the Canadiens' next two games. The Anahim Lake, B.C., native is considered day-to-day with the injury.
As a result, Peter Budaj will start Montreal's game against the Detroit Red Wings at Bell Centre on Wednesday.
Therrien's comment was news to Detroit coach Mike Babcock, who coached Canada to gold for a second straight time. Babcock said he was unaware of any Price injury.
The Habs visit Pittsburgh on Thursday and host the Toronto Maple Leafs on Hockey Night in Canada on Saturday.
The Canadiens are calling up Dustin Tokarski from the Hamilton Bulldogs in the American Hockey League to back up Budaj.
Price had two shutouts in his final two of five Olympic games as Canada's goalie at the Sochi Olympics. He sported a 0.59 goals-against average and .971 save percentage to help the team to Canada's third gold medal in men's hockey in the last four Olympics.
Price has a 26-17-5 record this season for the Canadiens, with a 2.33 goals-against average and .925 save percentage.