Fr Richard Rodgers, priest at St Mary's church in Cleland, North Lanarkshire, will be away from the parish for an 'unspecified period of time', said the Diocese of Motherwell.
A complaint about the 79-year-old was passed to police earlier this month and he's said to have agreed to the suspension.
The priest has moved out of the church house whilst the police investigation is carried out.
A spokesman for the Diocese of Motherwell said: "Following a complaint received by the Diocese of Motherwell and passed to Police Scotland, Fr Richard Rodgers, Parish Priest of St Mary's, Cleland, will not be in active Parish ministry for an unspecified period of time.
"Fr Rodgers has agreed to this and will not be living in the parish house or undertaking any public ministry.
"While the Diocese of Motherwell await the outcome of the police investigation, no further statements will be made."
A Police Scotland spokesman said: "We can confirm that we have received a report in connection with alleged historical sexual abuse and the matter is currently being investigated."