The slash occurred in the third period of the game and a match penalty for slashing (attempting to injure) was assessed on the play.
Kessel slashed Scott twice and gave him a spear, and he was ejected from the contest. His slash erupted into a benches-clearing brawl.
The league has said they endorse the use of a swinging stick for self-defense.
Brendan Shanahan, the league's Director of Player Safety, explained the suspension for Kessel.