Schwartz has not played since being injured on Dec. 29 against Philadelphia. He was a scratch in Seattle's next two games and the decision to have surgery was made with the Kraken on an extended break due to postponements.
The team said Schwartz will miss four to six weeks.
Schwartz has six goals and 14 assists in 29 games. He is tied for the team lead in assists and second on the Kraken in points.
Schwartz is the second big loss for Seattle's forward group, after Brandon Tanev was lost for the season to a torn knee ligament last month.
Because of postponements, Seattle is off until Monday when it plays at Colorado.