The incident occurred during Game Three of the playoff series between the teams on Monday when Cooke stuck out his knee and clipped Barrie, knocking him out of the contest.
Barrie suffered a left knee injury and is expected to be out of action for 4-6 weeks.
Minnesota went on to win the contest and holds a 2-1 advantage in the best-of-seven series with Game Four set for Thursday.
Cooke has 48 hours to appeal the suspension and if the terms of the ban are not fully served during the playoffs it will carry over to the start of the 2014-15 campaign.
(Writing by Jahmal Corner in Los Angeles; Editing by John O'Brien)
- Sports & Recreation
- Matt Cooke
- Minnesota Wild
- Tyson Barrie