Outspoken independent senator Nick Xenophon had warned he would identify the man if the Catholic Church of South Australia did not stand him down and launch an investigation into the alleged sexual abuse of Archbishop John Hepworth.
Archbishop Hepworth, who was trained and ordained as a Catholic but shifted to the Anglican church in the 1970s, claims he was repeatedly raped and sexually abused over a period of 12 years from age 15 by two priests and a seminary student.
Two of the men are now dead but the third, named by Mr Xenophon as Monsignor Ian Dempsey, runs a parish in South Australia.
Mr Xenophon claimed he was being protected by the Church and allowed to practise despite Mr Hepworth's allegations.
The Church has defended its decision not to suspend the priest, saying it was consistent with religious and procedural law, and implored Mr Xenophon to desist.
"The priest concerned has categorically denied the allegations and, objectively speaking, it is not irrelevant that he has been a priest of good standing in the archdiocese for almost 50 years," a legal letter from the Church said.
However, Mr Xenophon said the Church had given him "no choice" but to speak out.
He told an evening sitting of the senate that "sexual abuse flourishes because people keep secrets", before naming the accused priest.
The move has raised concerns in Australia over the use of parliamentary privilege.
Archbishop Hepworth, who is head of a breakaway Anglican group seeking reconciliation with the Vatican, had earlier called on Mr Xenophon not to name the man, saying he was "saddened" by the "very crude way" the issue was playing out.
"My allegations were a greater story than just this one priest. This treatment of this priest is only one part of that story," he told the Australian Broadcasting Corporation.
Archbishop Hepworth, who reported the abuse to the Archdiocese of Adelaide more than four years ago, broke his silence over the abuse he suffered at the weekend in an interview with the Australian newspaper.
He said that the abuse began one month after he entered Adelaide's St Francis Xavier Seminary to fulfil a childhood calling to train for the Catholic priesthood.
After more than a decade of predatory physical and emotional abuse, he fled to England and drove trucks before defecting to the Anglican Church.
He is believed to be the most senior church figure in the world to reveal he was a victim of clerical sex abuse.