Cole (rest) will not play Thursday in Winnipeg, according to John Lu of TSN.
Cole registered an assist and four shots on goal in Saturday's 7-4 win over the Sharks.
Cole is averaging 22:45 of ice time through his first three games with Vancouver.
Cole signed a one-year, $3 million deal with the Canucks on Saturday.
Cole has one assist, 12 blocks, 12 shots and seven hits in his last 10 games.
Cole has one assist, 14 hits and 11 blocks in his last six games.
Cole scored a goal and added an assist in Thursday's 4-1 win over Philadelphia.
Cole has one assist and is averaging 18:33 a game in nine contests this season.
Cole was cleared from his legal drama and made his season debut during the Lightning's 3-2 loss to the Flyers on Tuesday.
The NHL found no substantiating evidence in its investigation of Cole for allegations of sexual abuse made against him, TSN's Chris Johnston reports.