Michael Noonan is to retire from politics at the next election.
After Enda Kenny's resignation as Fine Gael leader and the race beginning for a new taoiseach, the Finance Minister said he did not want to be considered for another cabinet job and would not stand again for the Dail.
"I believe now is a good time for a new finance minister to take up office. Ireland is the fastest-growing economy in Europe, the budget is almost balanced and we are on the cusp of full employment," he said.
"I will continue to carry out my duties as Minister for Finance until a successor is appointed."
Mr Noonan made his announcement as Fine Gael deputy leader Dr James Reilly said he was stepping down from his role and declared his support for Housing Minister Simon Coveney for the party leadership.
Health Minister Simon Harris was one of the first cabinet members to declare his support for Mr Coveney.
Elsewhere, Tanaiste and Minister for Justice Frances Fitzgerald, who had been talked about as a possible candidate for the leadership, ruled herself out of the race.
Mr Kenny's successor is due to elected by the parliamentary party, rank-and-file members and councillors on June 2 with the new leader to be voted in as taoiseach in the Dail in subsequent days.