The hit came at 9:06 of the second period in Monday night's game after Hannan scored a goal. Colorado won the game 5-4.
Under the terms of the NHL labor agreement, and based on his average salary, Briere will forfeit $67,357, league officials said. The money will go to the Players' Emergency Assistance Fund.
Briere will miss games Wednesday against the New York Islanders and Friday at Buffalo. He will be eligible to return to action Saturday at Atlanta.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut