A team spokesman said Tuesday that Higgins sprained his left ankle and suffered ligament damage in Saturday's 2-1 loss to the New Jersey Devils.
The spokesman said surgery will not be required.
Entering play Tuesday night, Higgins, 23, led the Canadiens with 13 points (eight goals, five assists) in 13 games this season.
The six-foot 202-pound left-winger, a native of Smithtown, N.Y., was Montreal's first-round pick (14th overall) in the 2002 NHL entry draft.
Higgins has recorded 51 points (31-20) in 95 career regular-season games.