The 36-year-old has been sidelined with a lower-body injury and was moved to injured reserve on Wednesday.
Cooke has four goals and four assists in 27 games this season. Earlier in the season he missed 22 games due to a hip flexor muscle injury.
The veteran has spent 15 years in the NHL, previously playing for the Vancouver Canucks and Pittsburgh Penguins.
The Wild (24-20-6) host the Colorado Avalanche on Saturday.
- Molly Geary