Neither was available Saturday when the Bruins played at the Arizona Coyotes.
Chara, a 41-year-old defenseman, injured his left MCL in the first period of a 6-3 loss to the Colorado Avalanche on Wednesday. His leg appeared to buckle when he collided with Avalanche forward Carl Soderberg.
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The Bruins said Chara would be re-evaluated in four weeks.
Bergeron, a 33-year-old center, was injured in a 1-0 overtime loss at the Dallas Stars on Friday. He was checked along the board by Stars forward Radek Faksa in the second period, left the game, but returned to finish it.
Starting play Saturday, Bergeron was tied for second in the NHL with 26 points (nine goals, 17 assists), three behind Colorado Avalanche forward Mikko Rantanen.
Chara has four points (three goals, one assist) in 18 games this season, his 21st in the NHL.
Boston is also without defensemen Brandon Carlo (upper body), Charlie McAvoy (concussion), Kevan Miller (hand), John Moore (lower body) and Urho Vaakanainen (concussion).
The Bruins will be off until Wednesday, when they play at the Detroit Red Wings to begin a span of four games in six days.
