The case is the first known complaint to hit the diocese of Killala which covers large sections of Co Mayo and Co Sligo.
The elderly priest was suspended from parish duties by his bishop after a formal allegation was made against him.
The Irish Independent understands that the complaint of sexual abuse dates back to an incident in the diocese in the 1970s, and that it is being investigated by gardai and the HSE.
Last night, Bishop of Killala, John Fleming could not be contacted. And the priest, who voluntarily agreed to stand aside on being informed of the allegation, did not return a call made by the Irish Independent.
Geographically, the diocese of Killala takes in large sections of counties Mayo and Sligo, but it has a small Catholic population of 38,715.
The diocese has been struggling to stave off bankruptcy in recent years and its number of priests -- many of them elderly -- is declining.
Currently, Bishop Fleming is in charge of 70 priests, 10 of whom are retired, to minister for 22 parishes and 48 churches.
Last weekend, parishioners in the village in north Co Mayo were stunned to discover that their parish priest had left unexpectedly.
Mass-goers were informed of the investigation when a statement from the bishop was read out in the priest's parish last Saturday evening and Sunday morning.
The statement said Bishop Fleming had asked the priest to stand aside from his ministry while the allegation was being investigated.
The priest had agreed to do so, the statement added. "Since this complaint has not been established as either true or false, he enjoys the presumption of innocence during this investigation," read Bishop Fleming's statement.
Investigations
An Garda Siochana, church authorities and the HSE are now carrying out separate investigations into the complaint.
Bishop Fleming asked the congregation to pray for the person alleging abuse, the priest involved, their families, for the people of the parish and the diocese.
In the 2009 report of the Irish Catholic Church's independent National Board for Safeguarding Children, its chief executive Ian Elliott named Killala as one of the few dioceses which had not appointed a priest as its child protection delegate.
Nor had the diocese established child protection committees in parishes.
Last night, people in north Co Mayo were too shocked to talk openly about the complaint.
But one woman said that until now the people of the Killala diocese had not seen the need for a child protection delegate or for vigilance committees.
"Abuse allegations against clerics were unknown in this part of the world," she added.
One parishioner on hearing the complaint said the community was "in total disbelief" as the suspected priest was "such a nice man and is highly respected".
Meanwhile, members of the clergy have previously complained that the practice of removing a priest from office when a complaint is made, irrespective of whether he is later found to be guilty or innocent, marks their reputations for the rest of their lives.
SIC: II