The Canadiens announced on their Twitter feed that Drouin will be placed on long-term injured reserve by the club.
"We ask everyone to respect his privacy," the Canadiens said.
Drouin has 23 points in 44 games this season. He missed Montreal's past three games with a non-COVID-related illness.
The Canadiens, fourth in the North Division, are scheduled to host the division-leading Toronto Maple Leafs on Wednesday.