The hit occured five minutes into the third period of the Predators 5-1 loss to the Canucks.
Weber slammed Hansen into the glass behind the Nashville net with a blindside shoulder to the back. The Nashville blueliner received two minutes for boarding and an additional two minutes for unsportsmanlike conduct after he continued to argue about the penalty after it was assessed.
Hansen had a bloody nose after the play, but did not miss any game time due to further injury.
Brendan Shanahan, the NHL's director of player safety, released a statement about the incident and the punishment.
"On all plays we deem to be illegal there are varying degrees that escalate from one level to the next," said Shanahan in a statement. "I didn't like this hit, and I expressed that to Shea Weber. I feel it was an illegal hit. I would like to see less force in that situation and that is why he's being fined. He didn't use all of his force, and did get Hansen sort of on the right side of Hansen's body. I think a lot of Weber's impact and the sound was him hitting the glass. It wasn't square in the numbers, but it was illegal."
The $2,500 fine is the maximum allowable under the NHL's collective bargaining agreement.