Clarkson was automatically assessed the ban, which will keep him out of Toronto's first 10 games of the regular season, when he left the bench on Sunday night to participate in a brawl with the Buffalo Sabres.
He announced after the Maple Leafs' 3-2 loss to the Ottawa Senators that he would not appeal the decision.
"I sometimes make decisions with my heart, not my head," Clarkson said after the game.
Because the ban begins in the regular season, Clarkson was able to play against Ottawa. He will also be eligible to play in both of this weekend's preseason games against the Detroit Red Wings.
Maple Leafs coach Randy Carlyle said Clarkson will accompany the team to Montreal and Philadelphia for the Maple Leafs' first two regular-season games.
Toronto opens its season on Oct. 1 at Bell Centre.