If the suspension is not fully served in this year's playoffs, it will continue on next season. The Avalanche have a 2-1 series lead on the Wild with Game 4 on Thursday.
Cooke has 48 hours to appeal the decision, first to NHL commissioner Gary Bettman then if Bettman upholds six games or more, he then has seven days to file an appeal to a neutral arbitrator.
The incident occurred in the second period when Cooke and Barrie were involved in a knee-on-knee collision.
The suspension is the sixth of Cooke's career. After the incident he was assessed a two-minute minor for kneeing.
Coach Patrick Roy said after the Wild's 1-0 overtime win that Barrie has a medial collateral ligament injury in his left knee and will need four to six weeks to recover.
The offer of an in-person hearing gave the NHL the right to suspend Cooke for five games or more.
Barrie was one of Colorado's best offensive blueliners, with 13 goals and 25 assists in the regular season.
Matt Cooke's Suspension History:
Feb. 19, 2004: 2 games - Spearing (Matt Johnson, MIN)
Jan. 20, 2009: 2 games - Illegal check to head (Scott Walker, CAR)
Nov. 28, 2009: 2 games - Illegal check to head (Artem Anisimov, NYR)
Feb. 8, 2011: 4 games - Hit from behind (Fedor Tyutin, CBJ)
March 20, 2011: 17 games (10 regular season and first round of playoffs) - Elbow to the head (Ryan McDonagh, NYR)
April 23, 2014: 7 games - Kneeing (Tyson Barrie, COL)