Weber, 32, does not have any broken bones in his foot, but is still wearing a protective boot.
The NHL All-Star Game takes place on Jan. 28 in Tampa Bay.
Weber has been out of the lineup for the past seven games and has reportedly been battling the injury since the start of the season. He previously missed a six-game stretch at the end of November. The Sicamous, B.C., native has six goals and 10 assists in 26 games in 2017-18.
Montreal has struggled in Weber’s absence and is currently mired in a five-game losing streak. The Canadiens sit sixth in the Atlantic Division with 36 points through 40 games.