Vermette slashed at the leg of linesman Shandor Alphonso after losing a faceoff with 7:33 of the third period to earn a 10-minute penalty for game misconduct.
In addition to the ejection, Vermette could face further discipline.
Per the NHL's Rule 40.3, deliberately applying physical force to an official in any manner comes with an automatic 10-game suspension.
Calgary Flames defenseman Dennis Wideman was suspended 20 games for abuse of an official last season, after cross-checking a ref on his way back to the bench. Wideman's suspension was later reduced to 10 games through an appeal.
The Ducks won Tuesday night's game 1-0.
In his first season with the Ducks, Vermette has eight goals and 14 points in 57 games.