Suarez, the league's top scorer with 23 goals, has been widely condemned for his behaviour in Sunday's 2-2 draw and is expected to get a lengthy ban from the Football Association but Liverpool managing director Ian Ayre said the club would stand by him.
"I think the most important thing is that we acted swiftly yesterday," Ayre told the club's website.
"Luis issued his apology and then we spoke with him last night and then again this morning. We've taken action to fine Luis for his actions."
Ayre did not specify the size of the fine but Suarez asked for the money to be donated to the Hillsborough Family Support Group - an organisation set up after the 1989 stadium disaster that left 96 Liverpool fans dead.
Former Liverpool midfielder Graeme Souness said on Sunday that Suarez had reached "last chance saloon" at Anfield after the latest in a string of misdemeanours while others have suggested the club could take a moral stance and terminate his contract.
However, Ayre said manager Brendan Rodgers would work with the player to help improve his discipline.
"The owners are happy with the way we are handling the matter," said the managing director.
"He's a very popular player with his team-mates. As we keep saying, he signed a new four-year contract last summer and we'd all love to see him here throughout that contract.
"He's a fantastic player, top scorer and everything we'd want in a striker so there's no change there."
The Professional Footballers Association (PFA) said on Monday that Suarez would be offered anger management classes.
