The Canadiens' captain was injured six minutes into the first period. Weber winced in pain on the bench but played seven more shifts and finished the first period. He did not return for the second period.
The 33-year-old already missed the first 24 games of the season with foot and knee injuries dating to last season.
After the game, Montreal head coach Claude Julien told reporters that Weber will make the trip with the team to Detroit but that he cannot guarantee if Weber will play on Tuesday.
Information from The Associated Press was used in this report.