"We'll know more tomorrow after he sees the doctors, but you've got to figure at least three weeks," Stars coach Jim Montgomery said after the game.
"We're hoping for the best, but we think it's going to be a while."
Klingberg, who has five goals and eight assists in 15 games this season, is the latest Dallas defenseman to be sidelined because of injury, joining Connor Carrick (foot), Marc Methot (lower body) and Stephen Johns (post-traumatic headaches). The team's AHL affiliate is also dealing with a banged up defensive corps, including Gavin Bayreuther.
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This post has been updated. DallasStars.com's Mark Stepneski contributed to this report.