The Russian suffered the injury as he tried to check Milan Lucic of the Boston Bruins on Saturday.
Emelin, 26, has three goals and nine assists in 38 games in his second NHL season.
Last season, he had three goals and four assists in 67 games.
The Canadiens also announced the recall of Nathan Beaulieu to replace Emelin.
Beaulieu practised with Francis Bouillon on Monday, while Davis Drewiske, who was obtained from the Los Angeles Kings last week, replaced Emelin alongside Andrei Markov.