The forward, who hasn't played since April 21, was placed on long-term injured reserve Wednesday. He scored 23 points (two goals, 21 assists) in 44 games this season.
"The most important thing right now is 'Jo' taking care of what he needs to take care of," Canadiens coach Dominique Ducharme said Wednesday. "When I heard his name this morning, I don't think hockey, I think about the person.
"I'm not going to get into the details. All that I wish for him is that he does what he needs to do, that he takes care of his business. We are with him, we support him, his teammates support him. We're a team and we're going to remain a team."
Drouin missed three games because of a non-COVID-19 related illness, but Ducharme said that wasn't the reason for him taking a leave.
"No, it's not related at all," Ducharme said. "They are personal reasons and we need to respect that. … It's his personal life and we're there to support him, so we will support him. ... We had discussions, it was the right thing for Jonathan to do. … I have discussions with my players every day. I like to know how they feel. We are here to get the best out of them but also to help them. We are there for them as people. We will always be there for them."
Montreal (21-18-9) is fourth in the seven-team Scotia North Division, six points ahead of the fifth-place Calgary Flames for the final Stanley Cup Playoff berth. The Toronto Maple Leafs defeated the Canadiens 4-1 on Wednesday to become the first North team to qualify.
Drouin is in his fourth season with the Canadiens. He was limited to 27 games last season because of a wrist injury and scored 15 points (seven goals, eight assists).
"I don't want to go into details," Canadiens forward Phillip Danault said. "It's a delicate situation, it's his private life. It's not easy. … We're sad for Jo. … I know what it's like to play in Montreal. This is his life. I worry about Jo. He's my friend. We are Quebecers together in Montreal. But sometimes there are things more important than hockey."
Selected by the Tampa Bay Lightning with the No. 3 pick in the 2013 NHL Draft, Drouin has scored 232 points (69 goals, 163 assists) in 393 regular-season games for the Canadiens and Lightning and 21 points (six goals, 15 assists) in 33 playoff games.
"We're definitely going to miss him, he's a great teammate, unbelievable player," Canadiens forward Jake Evans said. "Loves the game and he's a really fun person to be around."
NHL.com columnist Dave Stubbs and independent correspondent Sean Farrell contributed to this report
