Suarez, 26, has apologised for his "inexcusable behaviour" after the incident during Sunday's 2-2 draw at Anfield, which saw him tangle with Ivanovic in the penalty area midway through the second half and bite the defender on the arm.
Referee Kevin Friend did not see the incident and the Football Association is set to open an investigation into the matter on Monday, while police have confirmed Ivanovic will not press charges.
Liverpool have already fined Suarez and the money will go to the Hillsborough Family Support Group, whose chairman Margaret Aspinall said: "It is a nice gesture but it is a terrible thing under the circumstances. We would rather him not have done that at all."
The Uruguayan wrote on his Twitter page: "For my unacceptable behaviour the club has fined me.
"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."
It is the latest in a series of unsavoury incidents in Suarez's career - including a previous biting incident in Holland - and PFA chief executive Gordon Taylor said the players' union would offer the striker help to deal with his temper.
"There is no doubting his football ability, that's why it is so disappointing and embarrassing when he lets himself down," said Taylor.
"We have to work hard on anger management now. We have trained counsellors in this field and we will be offering their services to Liverpool and the player to try to improve matters."
Suarez is also one of the candidates for the PFA Player of the Year award to be announced on Sunday, and Taylor confirmed that the latest controversy would not affect his position on the shortlist.
Taylor added: "It's decided on votes and it is a football matter but of course it is embarrassing that it should happen."
Suarez made a dramatic late impact on the match at Anfield, scoring in injury time to snatch Liverpool a draw.
Chelsea had twice led, through Oscar and Eden Hazard, with Daniel Sturridge scoring Liverpool's first equaliser.