The artist was arrested at Shannon Airport in November 2014 when she was taken off a flight from New York after an alleged air rage incident.
As she was being detained, O'Riordan told officers that she was an "icon" and the "Queen of Limerick".
Last December, she admitted three assaults and obstructing an officer.
She was diagnosed as suffering bipolar disorder after the incident.
Medical reports given to the court showed she had been suffering mania and was mentally ill when it happened.
At Ennis District Court in County Clare on Wednesday, a judge said it would be unfair to impose a criminal conviction on O'Riordan.
He accepted O'Riordan has no memory of the incident and had a "very severe medical illness which completely inhibited her judgment".
"Let me be utterly clear that the defendant is not being treated any differently than anyone else," he said.
The judge asked for the money to be paid to a charity that helps prisoners ahead of their release from jail.
Originally from County Limerick, O'Riordan became a multi award-winning musician after first singing with the Cranberries when she was just 18.
The band went on to become one of the biggest of the 1990s, selling tens of millions of records.
Leaving the courthouse, O'Riordan said she was feeling "very positive about this coming year".
She added: "I have a couple of albums coming out and I'm going to go back to work."
Cranberries singer Dolores O'Riordan has been ordered to give 6,000 euros (£4,690) to charity after head-butting an Irish police officer.