O'Dea gave the false information to a journalist last year about Limerick Sinn Fein councilor Maurice Quinlivan.
He told a journalist for the Limerick Leader: "I'd like to ask Mr Quinlivan, is the brothel still closed?"
Later O'Dea made a statement under oath denying he had said this but when he found the interview had been taped he admitted he had done so, essentially admitting to perjury.
Two months ago he agreed at the High Court to pay damages to Quinlivan.
In his resignation letter, O'Dea stated that staying in office would "distract from the important and vital work of the government.""
In a debate in the Irish parliament yesterday he had defended his role.
"Having seen the transcript, I took the initiative - I went to my solicitor and immediately corrected my affidavit," he said.
"I was not forced or pressed to do this. I did so of my own volition as I then knew that my original affidavit was wrong."
He claimed he had been tipped off about the brothel by a police officer.
John Gormley, leader of the Green Party, the junior coalition government partner, pulled the plug on O'Dea after accusing him of misleading statements.
"At the very conclusion of yesterday's Dail debate, Mr. O'Dea said his original actions in the matter were based on information given to him by An Garda Siochana (the police)," he said.
"We were very concerned by this behavior by a member of government. We have also taken the view that Willie O'Dea's comments and conduct during yesterday's debate and in subsequent media appearances were inappropriate.
"All these factors have led us to conclude that Willie O'Dea could not continue as a member of this government."
Opposition Fine Gael party leader Enda Kenny said the credibility of the coalition cabinet was "in tatters."
"Despite knowing the full facts, the Taoiseach and his Fianna Fail and Green ministers queued up just yesterday to vehemently support Deputy O'Dea, to assert that he had done nothing wrong other than a simple human mistake, and to vote complete confidence in him."