The league announced the discipline Tuesday.
The incident occurred at 9:06 of the second period Monday night, right after Hannan had scored.
Briere will miss games Wednesday against the New York Islanders and Friday at Buffalo. He will be eligible to return Saturday at Atlanta.
He will forfeit $67,358 in pay, with the money going to the Players' Emergency Assistance Fund.
Briere says he respects the decision and will try to move on once he's back.