The Wild also placed goalie Josh Harding, who leads the NHL with a 1.66 goals-against average, on injured reserve with an unspecified illness.
Koivu, who has 35 points in 44 games, was hit by a puck Saturday against Washington. The Wild said the operation went as planned and Koivu was expected to be fully recovered and playing again in approximately four weeks.
Koivu has eight goals and 27 assists. He's third among NHL forwards in time on ice with an average of 21 minutes and 34 seconds per game.
The Wild play at Los Angeles Tuesday, and left wing Zach Parise and defenseman Jared Spurgeon are already on injured reserve with foot injuries. Harding has missed the last two games as he's been adjusting to new medication for multiple sclerosis.