The incident occurred with 12:27 to play in the third period of the road game when Vermette swung his stick at Alphonso and made contact with the official's leg after losing a faceoff.
Vermette was given a game misconduct and the Ducks are bracing for further action from the NHL.
Ducks coach Randy Carlyle said Vermette was not being malicious in striking the linesman but was reacting to not being ready for the dropping of the puck.
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"He touched the official. What are you going to do?" Carlyle told the Orange County Register after the Ducks defeated the Wild 1-0.
"These are things that the league reviews. We have a view on it; they have a view on it. Whatever they decide, we have to live with."
According to NHL rules, deliberately applying physical force to an official in any manner is worthy of an automatic 10-game suspension.
Vermette, 34, is in his first season with Anaheim (30-18-10) and has played in all 58 of the team's games, scoring eight goals. (Writing by Jahmal Corner in Los Angeles; Editing by John O'Brien)
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