Unseen by match officials, the 26-year-old lashed out at the arm of the Serbian in the 2-2 draw at Anfield, with the Professional Footballers Association since announcing the group is to offer the striker anger management counseling.
Suarez tweeted: "For my unacceptable behavior yesterday the club has fined me today, I have asked the club to donate the money to the Hillsborough Family Support Group for the inconvenience I have created to the Liverpool fans and to Ivanovic."
Speaking after the game yesterday, Liverpool manager Brendan Rodgers and managing director Ian Ayre hinted that the club would take action against Suarez.
Ayre, who cancelled a trip to Australia in order to personally deal with the matter, said the incident did not "befit" the behavior of a Liverpool player.
"Luis is aware that he has let himself and everyone associated with the club down," Ayre told the club's official website.
"We will deal with the matter internally and await any action from the Football Association."
The Football Association has yet to announce its own course of action, but Suarez will likely face a lengthy ban.