Bergeron was a game-time decision for Boston's Game 1 victory on Monday but didn't end up taking the pregame skate. The center left the Bruins' regular-season finale at Montreal with an upper-body injury and was battling an illness that had swept through the Boston dressing room.
Montgomery said Bergeron was "feeling better," but he did not participate in an optional skate on Tuesday morning.
Bergeron, 37, had 58 points in 78 games this season. He's considered the best defensive forward in the NHL, having won the Selke Trophy a record five times.
Center Pavel Zacha replaced Bergeron on the Bruins' top line with Brad Marchand and Jake DeBrusk in Game 1. That line was paired against Panthers star Aleksander Barkov, who didn't record a point or have a shot on goal in the game.
"It's two lines against each other. You always want to win that battle," Zacha said. "So that's the exciting part for me: To be in those positions to play against those lines."
Florida Panthers coach Paul Maurice said Barkov needs to learn to "grind a playoff game" rather than try to score coast-to-coast, which played into the Bruins' hands in Game 1.
Zacha said Bergeron has helped him behind the scenes on faceoffs and in getting him in the right mindset for the playoffs. "I talked to him a little bit. I just told him that I didn't play in the playoffs in a while and he calmed me down. Just play, have fun there and battle hard," he said.
Zacha had the best season of his eight-year NHL career with Boston, having been traded there by the New Jersey Devils for Erik Haula last offseason. He had 21 goals and 36 assists in 82 games, all career highs.
Bruins winger Taylor Hall was teammates with Zacha when they were both with the Devils.
"I played with him in Jersey and I saw the potential that he had. Quite frankly, I saw him not really have a role there and not really have an identity as a player that was given to him," Hall said. "I think once he got here, he was coached very well, he was given a lot of opportunity and he made the best of it. He's a great guy and he works hard. To see his growth from Jersey until now, it's been awesome for our team."
Game 2 is in Boston on Wednesday night.
Maurice would not name a starter for the Panthers in goal, as Alex Lyon gave up three goals on 29 shots in his playoff debut. Two-time Vezina Trophy winner Sergei Bobrovsky, who has appeared in 51 playoff games, was his backup.
"I think he was fantastic last night. I loved his game," Maurice said of Lyon.