The league announced the decision Friday after the department of player safety reviewed the play. Rupp hit Oshie with a shoulder to the head in the second period of the Wild's 4-2 victory over the Blues. He was issued a match penalty for attempt to injure.
Rupp will lose $7,692.31 for the four-game suspension, which includes the regular-season finale Sunday and the Wild's first three playoff games.
The seldom-used veteran forward is counted on to bring grit and toughness when called upon. Prior to the game against the Blues, Rupp had not played since Feb. 1.