Clowe was penalized for his actions at the conclusion of Friday's 2-1 San Jose loss, during which he left his team's bench and skated directly over to Blackhawks forward Andrew Shaw -- who was in the process of leaving the ice -- and grappled with him while game officials immediately intervened.
The altercation apparently was precipitated by Shaw's heavy hit into the boards of Clowe's teammate, Joe Pavelski.
Clowe was initially assessed a game misconduct for leaving the bench for illegally leaving the bench, which would have meant an automatic 10-game suspension and $10,000 fine for the 30-year-old.
But NHL discipline chief Brendan Shanahan instead determined Clowe had entered the ice on a legal line change, and so was assessed only a two-game penalty.
The Sharks player -- who twice previously been fined for illegal conduct -- missed Saturday's 3-1 loss in Dallas and now will also be absent for Tuesday's home contest against Colorado.