The forward won't play against the Edmonton Oilers if there are games Wednesday and Friday. The game scheduled for Monday between Edmonton and Montreal was postponed because Canadiens forwards Joel Armia and Jesperi Kotkaniemi entered NHL COVID-19 protocol.
Toffoli leads Montreal with 18 goals and is tied for first in points (27) with defenseman Jeff Petry.
Canadiens coach Dominique Ducharme said Toffoli could return as soon as their home game against the Ottawa Senators on Sunday.
"He will be evaluated and in the days that follow the series against the Oilers, we think he'll be able to return," Ducharme said.
Ducharme said Toffoli was injured late in a 3-2 overtime loss to the Vancouver Canucks on Friday. He played one shift in overtime that ended with 3:35 remaining.
"We didn't think he would be available for overtime," Ducharme said. "He went on the ice before it started and he told me he was OK for overtime, then in the hours that followed, the next day too, he had tests. He was warmed up that night so he didn't feel it as much. But the next day it was worse."
Toffoli did not play in a 5-4 shootout win against the Canucks on Saturday.
Montreal (14-8-9) is fourth in the seven-team Scotia North Division, two points ahead of the Canucks (16-16-3), who have played four more games. The top four teams in the division will make the Stanley Cup Playoffs.
NHL.com independent correspondent Sean Farrell contributed to this report
