The Broadcasting Authority of Ireland is to investigate the circumstances that led to false allegations being made against Fr Kevin Reynolds by RTÉ.
The Cabinet discussed the matter and decided that there should be "an independent inquiry to determine the true facts and circumstances" that led to the programme being broadcast.
Minister for Communications Pat Rabbitte has asked the BAI's Compliance Committee to examine if RTÉ "met its statutory responsibilities around objectivity, impartiality and fairness".
The Government said it expects a report to be delivered within two months.
The Association of Catholic Priests has welcomed the announcement of an investigation.
Its spokesman, Father Sean McDonagh said the decision was a proper one because the injustice done to Fr Reynolds was so serious.
Fr McDonagh said the investigation would be an opportunity to review the perceived anti-Catholic bias within RTÉ and the media in general.
He said the Association did not want to scapegoat any individual involved in the offending Prime Time Investigates programme nor did it want to see the end of robust investigative reporting.
Bishop of Elphin Dr Christopher Jones also welcomed the announcement that the Cabinet had discussed the matter.
Speaking earlier, Fine Gael Senator Michael Mullins said large amounts of taxpayers' money had to be spent in order to repair the damage done as a result of the programme and he said the minister should cut funding to RTÉ appropriately.
Senator Mullins said irreparable damage had been done to Fr Reynolds' reputation and he said there were other allegations of defamation in the programme against a person who is now deceased.
He said he had been provided with information that calls into question the basis on which the programme was made.
Fine Gael Senator Martin Conway has called on Senator Mullins to hand over the additional information to gardaí.
Senator Conway said the information should be made available for a criminal investigation to be conducted.
He said it was time for serious reflection on the powers of the press in general.
Independent Senator John Crown called for information on who imposed a 'gagging order' on the terms of the settlement.
He said public bodies should be prevented from imposing such orders.