The team says full recovery is expected to take five to six months. General manager Jarmo Kekalainen says Werenski will be ready "by the start of the season or shortly thereafter."
Werenski, 20, underwent the procedure on Thursday in Columbus.
He said after the playoffs that the injury from a game in October affected his slap shot the rest of the season.
Still, he and Seth Jones each scored 16 goals, a franchise record for defensemen and fourth in the NHL among blueliners. Werenski has 27 goals and 57 assists in 155 career NHL games over the past two seasons.