Cowan, who was hurt late in Game 3, will be out for an indefinite period, according to the team.
Cowan, a tough guy picked up off waivers from Los Angeles on Dec. 30, was playing on the second line in the playoffs and scored two of Vancouver's five goals in this series, which the Ducks led two games to one. He had the double-overtime winner in Game 2 in Anaheim.
Cowan had seven goals, three assists and 93 penalty minutes in 47 games with the Canucks in the regular season.
Vancouver has also been missing gritty forwards Matt Cooke (groin) and Ryan Kesler (broken finger) since the first game of the first round.
The Canucks did get back defenceman Kevin Bieksa, who hadn't played since Game 7 against Dallas in the first round, from an undisclosed injury for Game 4.