The suspension was announced Monday by the league's Department of Player Safety.
Clowe was assessed a minor penalty for roughing and a game misconduct for leaving the bench on an illegal line change to start a fight with Blackhawks forward Andrew Shaw with 8.4 seconds left in regulation—an infraction that calls for a 10-game suspension.
But upon further review the line change was deemed legal. Clowe then skated directly at Shaw, who was not engaged with any other player, grabbed him and wrestled him to the ice.
Clowe, who will forfeit $39,189, missed San Jose's 3-1 loss to Dallas on Saturday and will also sit out Tuesday's game against Colorado. He is eligible to return Thursday against Detroit.