The incident occurred Friday night in the Maple Leafs' 9-3 win in Atlanta.
Eager received a match penalty on the play.
He will forfeit $20,752.68 in salary, which will go to the Players' Emergency Assistance Fund.
Eager's overall performance had a huge, detrimental effect on the Thrashers' game plan. His four penalty minutes late in the first period for roughing and cross-checking led to a power-play goal by Mikhail Grabovski, giving the Maple Leafs a 2-1 lead.
Eager is eligible to return Jan. 20 against Tampa Bay.
Pierre LeBrun covers the NHL for ESPN.com. Information from The Associated Press was used in this report.