The 36-year-old blue-liner left the ice early in the first period and didn't return to the game.
The Canadiens confirmed Weaver would not return against the Stars on their Twitter page.
This is Weaver's second year with Montreal. He joined the team last season for their playoff run. The veteran has played with five teams over his 10-year NHL career.
Garbutt already served a two-game suspension last month for his hit on Edmonton forward Taylor Hall.
Last season, Garbutt was banned five games for boarding Dustin Penner.