The league's department of player safety announced the punishment Tuesday.
Dillon was given a major penalty and game misconduct Monday night for slashing Bowey with five seconds left in the third period of San Jose's 4-1 loss to the Capitals.
The Sharks' next game is Thursday night against the Carolina Hurricanes.
Dillon will forfeit $17,580.65 of his salary. The money goes to the Players' Emergency Assistance Fund.