Coach Claude Julien said that the defenseman was injured in Tuesday's game against the Devils. Weber will miss at least a week.
Weber, 34, had represented the team at the All-Star Game and had won the hardest shot competition for the third time. He has 13 goals and 21 assists this season.
The Canadiens have battled injuries all season, but they had gone 7-3 in their past 10 games to climb within eight points of the second wild card in the East.