Clowe has been offered an in-person hearing on Monday to discuss the incident, and he could be facing a 10-game suspension. The fact the NHL offered a hearing in person means the league can suspend him for more than five games.
With under a minute to play in the game, Shaw was penalized for boarding Joe Pavelski in front of the San Jose bench. Clowe then came off the bench during the ensuing stoppage and became involved in a skirmish with Shaw. The linesman stopped it before it could turn into a fight.
Clowe was given a two-minute minor for roughing and a game-misconduct. If the league determines Clowe acted illegally and came off the bench for the purpose of starting a fight, he's going to be sitting out for quite a while.
According to NHL rule 70.1, "No player or goalkeeper may leave the players' or penalty bench at any time during an altercation or for the purpose of starting an altercation. Substitutions made prior to the altercation shall be permitted provided the players so substituting do not enter the altercation."
The incident can be seen in the video posted above via CSN Chicago.
It's not the first time Clowe has created some trouble for himself when it comes to plays involving the bench. He avoided suppplementary discipline last season for playing a puck from the bench to break up a Los Angeles Kings rush.