The defenseman was injured in a 4-3 win against the San Jose Sharks on Thursday. He left the game at 6:04 of the third period after blocking a shot.
"[We will miss] his skills, how he can break out the puck alone," defenseman partner Esa Lindell said. "His jokes and his presence in the locker room too."
Klingberg, 26, has 13 points (five goals, eight assists) in 16 games this season. He tied Brent Burns of the San Jose Sharks for second among defensemen with 67 points (eight goals, 59 assists) last season, one behind John Carlson of the Washington Capitals.
Defenseman Joel Hanley was recalled from Texas of the American Hockey League. He will play against the Nashville Predators at American Airlines Center on Saturday (2 p.m. ET; FS-SW, FS-TN, NHL.TV).
Stars coach Jim Montgomery said rookie defenseman Miro Heiskanen will take Klingberg's spot on the top power-play unit, and that all of their defensemen will need to step up in Klingberg's absence.
"Here's your opportunity to show everybody that you can be not just a regular NHL player, but a player to be reckoned with in the NHL," Montgomery said.
