Price appeared to be hurt late in the third period Tuesday night in the Senators' 3-2 overtime win and was replaced with Peter Budaj for the extra period.
Price, 25, made 30 saves for the Canadiens in Game 4, two nights after allowing all six goals in Ottawa's 6-1 victory in Game 3.
The three-time All-Star finished the regular season with a 21-13 record.
The Senators lead the series three games to one. Game 5 is Thursday night in Montreal, with Budaj set to make his first career playoff start. Robert Mayer of the AHL Hamilton Bulldogs is his backup.
The Canadiens have been hit hard by injuries. A day earlier, captain Brian Gionta was ruled out for the rest of the playoffs with a torn left biceps tendon. He is to have surgery Friday. Also injured are forwards Lars Eller, Brandon Prust and Ryan White.
Information from The Associated Press was used in this report.