The Canadiens made the announcement after a 4-3 overtime loss to the Vegas Golden Knights on Thursday.
Allen was hurt on Jan. 12 against the Boston Bruins.
Allen is 5-16-2 with a 3.15 goals-against average and .901 save percentage this season.
The native of Fredericton, N.B. has been the No. 1 goalie for Montreal this season with Carey Price out.