Weber, who practised Tuesday morning in Dallas, did not take part in the pre-game warm up. In 20 games this season, he has four goals and nine assists.
Weber recently missed a game against the Minnesota Wild in Montreal on Nov. 9 with an upper-body injury. He also left practice early on Monday before the team departed for Dallas.
The Canadiens are scheduled to travel to Nashville Tuesday, where they will take on the Predators.
Weber spent the first 11 seasons of his NHL career as a member of the Predators before being traded to Montreal in June of 2016.