Clarkson received an automatic 10-game suspension from the NHL -- that doesn't begin until the regular season -- for leaving the bench to join a fight.
Clarkson is allowed to play in preseason games, including Tuesday night's home game.
Kessel had a telephone disciplinary hearing on Tuesday regarding his actions in Sunday's game.
Kessel slashed Scott twice and gave him a spear, resulting in his ejection from the game. That sparked the bench-clearing brawl that led to Clarkson's long regular-season ban.
Kessel's clean record and the fact that Scott wasn't injured determined the suspension, according to NHL vice president of player safety Brendan Shanahan.
"While we acknowledged that Kessel's initial motivation was self-defense, he persists and swings his stick again even having escaped the immediate threat from Scott," Shanahan said.
Kessel was to sit out Tuesday night's preseason home game, but is expected to be in the Maple Leafs lineup for Toronto's regular-season opener at Montreal on Oct. 1.
Toronto coach Randy Carlyle says it is important for Clarkson to play as much as possible before he is forced to sit out.
Clarkson will travel with the Maple Leafs to Montreal and Philadelphia for their first two regular-season games and practice.
Also Tuesday, Sabres coach Ron Rolston was fined an undisclosed amount for his role in the melee -- infractions the NHL described as "player selection and team conduct."