The NHL said Clarkson was sanctioned for delivering a hit to the Blues forward's head in the second period of Toronto's 6-3 Thursday loss to St. Louis.
Game officials whistled Clarkson for a minor penalty after the check.
The 29-year-old, who in July signed a seven-year with Toronto as a free agent, earlier drew a 10-game suspension for his part in a pre-season brawl between the Leafs and the Buffalo Sabres.
Clarkson has produced just two goals and four assists over 23 games since coming to Toronto from the New Jersey Devils.
He will be eligible to return in Tuesday's against Florida.