"There was one player that the test came back positive and there was close contact, so the League didn't want to take any chances," Bergevin said. "And then we retested again and it came back (positive) again. But so far it hasn't spread, so if we keep the same pace until Monday afternoon we should be OK to come back."
The home games at Bell Centre, against the Edmonton Oilers on March 22, March 24 and March 25, and against the Ottawa Senators on Sunday, were postponed and will be rescheduled.
They were the first games postponed this season in the Scotia North Division, which is made up of the seven NHL teams based in Canada.
Montreal's next scheduled game is at Ottawa on Tuesday.
Canadiens forwards Jesperi Kotkaniemi and Joel Armia were placed in NHL COVID-19 protocol on March 22. Montreal's practice facility has been closed since then.
Bergevin said the player who tested positive is in isolation and had contracted a variant of the virus.
"What I know is that we did tracing and there were more than two players who had close contact, so they didn't take any chances for the players' sake, also for the Edmonton Oilers' sake," Bergevin said. "So that's why the precautions were taken and I think it was the right decision."
The Canadiens have been limited to off-ice workouts and remote meetings.
"The positive side is that it will allow our injured players time to get better and all of our players to rest," Bergevin said. "But we need to be in game shape and we can't skate for seven days. We've got them on bikes and in seminars with our training staff every day to keep them in good physical condition as best we can."
Bergevin said players were given workout plans and coach Dominique Ducharme was conducting seminars remotely.
The GM said he discussed plans to reschedule the postponed games with the NHL on Wednesday. Due to the coronavirus pandemic, the NHL is playing a condensed 56-game season that started Jan. 13 and is schedule to end May 10.
"It's not going to be easy but I can only control what I can control," Bergevin said. "The League and the [NHL] Players' Association made a decision to get those 56 games in 116 days with the possibility of missing games because of that reason. So it's something that we have to deal with.
"Obviously it's not ideal, but it's happened to other teams in the United States so we're going to manage this situation the best we can."
There have been 46 games postponed since the NHL season began Jan. 13, including 41 because of protocol. Five games have been postponed because of weather-related issues.