Suter will miss Minnesota's game Thursday night in Buffalo against the Sabres and Saturday at home against the Arizona Coyotes.
The 29-year-old had never been suspended before in his 10-year career.
Suter said Tuesday night after the Wild's loss in Pittsburgh that the elbow was accidental.
Coach Mike Yeo backed him up on that Wednesday, speaking before Suter's disciplinary hearing.
"What I saw when I looked at it initially is he's not looking at the player at all," Yeo said after the Wild's practice at First Niagara Center. "He's looking at the player and I think he puts his elbow up just almost kind of to box the guy out."
No one plays more than Suter, as he averages a league-high 29:34 a game, just ahead of Drew Doughty of the Los Angeles Kings.
The argument could be made that no team needs one single skater more than the Wild need Suter, especially considering they've lost six in a row and 12 of their past 14 games.
Yeo was hoping Suter would just be fined by the NHL, as Marco Scandella was earlier in the season.
"I would hope for sure, for a lot of reasons," Yeo said. "I know that that's not his intention, that's not the type of player that he is, and i know that he felt bad about it even during the game. As much as anything else, we need him in the lineup."
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