The Predators announced the surgeries Thursday.
Wilson has not played since he hurt his shoulder March 9 in a game against Minnesota when he was the team's leading scorer with seven goals and 19 points. He tried skating with Nashville on Tuesday, but the Predators currently rank 13th in the Western Conference having lost four straight games.
Gaustad is Nashville's key forward handling faceoffs. But he has missed 17 games this season with injuries and will have his shoulder surgically repaired. Bourque had missed the past five games and will have a knee surgery.