Gallagher, 28, was injured after being cross-checked near the chin by Philadelphia Flyers defenseman Matt Niskanen in the third period of Game 5 of their Eastern Conference first-round series on Wednesday in Toronto.
Gallagher was bleeding from his mouth following the hit by Niskanen, who was not whistled for a penalty. Niskanen, however, will have a hearing with the NHL Department of Player Safety on Thursday.
Gallagher's availability for Friday's Game 6 of the series is not immediately known. The Flyers hold a 3-2 edge in the series.
"We're still waiting for feedback medically," Canadiens interim coach Kirk Muller told reporters in the team's Zoom call on Thursday.
Gallagher, who shared the team lead in goals (22) with Tomas Tatar in the regular season, scored for the first time in the playoffs in Montreal's 5-3 victory over Philadelphia on Wednesday.
Niskanen, 33, has yet to record a point but sports a plus-2 rating in eight games this postseason.
--Field Level Media