Cullen was hurt in Monday's loss to St. Louis.
The Wild play at San Jose on Wednesday and at Los Angeles on Thursday. Coach Mike Yeo said after practice on Tuesday that Cullen's injury doesn't appear to be serious. Yeo said he's hopeful that Cullen can play at Columbus on Sunday.
The 36-year-old Cullen had four goals and 12 assists over a 16-game stretch through March 30. He's fourth on the team with 25 points this season, including seven goals.
To fill his slot, the Wild recalled forward Johan Larsson from the AHL Houston Aeros. The 20-year-old made his NHL debut against Detroit Feb. 17.