According to the Belfast Telegraph Hugh Kennedy, 59, was working as Administrator at St Peter's Cathedral in Belfast (above) until this year before working at More House, a Christian school in the Archdiocese of Westminster in London.
Before going to St Peter's Cathedral in 2006 he served as a parish priest in north Belfast.
Fr Kennedy is also known for appearing in the BBC documentary Choirboys, which looked at the efforts of St Peter's Cathedral's choir as it worked up to performing for the Pope at the Vatican.
PSNI Detective Inspector Zoe McKee said: "We have been informed that the PSNI has initiated an investigation into an alleged incident of an historical adult nature involving a priest of the Diocese of Down and Connor.
"Inquiries into this matter are ongoing."
The Diocese of Down and Connor said in a statement: "Bishop Noel Treanor has suspended the cleric's ministry pending a full and complete investigation.
"As with every person in such circumstances the cleric's innocence is presumed until the contrary is proven and he retains the right to his good name."