The 82-year-old clergyman, interviewed under caution, has been named in news reports as Canon Mortimer Stanley.
The investigation relates to the indecent assault and sexual abuse of three women during their time as schoolgirls at St Vincent's Primary School in Norden, Rochdale, between 1980 and 2000, Greater Manchester Police said.
It is understood the allegations involve a parish priest at St Vincent de Paul RC Church who was serving at the time of the alleged offences. The church is located in the same grounds as the school.
The offences did not occur within the school but at an adjacent presbytery, police said.
Detective Constable Christian Chivers, from Greater Manchester Police's Public Protection Investigation Unit, said: "I want to reassure local residents, and more importantly parents of children currently at St Vincent's, that these are historical incidents.
"While we do not believe there is any reason for current pupils or their families to be unduly concerned, this is extremely serious and upsetting for the victims in this case, who we are continuing to provide specialist support to.
"The safeguarding of pupils is without doubt a top priority for us, the school and Salford Diocese and we are working together as part of this investigation.
"As part of this investigation I am appealing to former pupils who may have information about the offences under investigation or who may want to speak to us about similar matters to come forward.
"I want to reassure anyone who might want to report any incidents or offences that we treat all allegations of sexual abuse extremely seriously and in the strictest confidence and we have officers on hand to deal with your complaints swiftly and sympathetically."
In a statement, the Salford Diocese said: "We have been made aware that there is an ongoing police investigation into allegations of historical sexual abuse at St Vincent's, Norden.
"The Diocese is co-operating fully with the police and the statutory agencies in these investigations in line with the robust safeguarding policies put in place by the Catholic Church in this country in recent years."
Anyone with information is asked to call police on 101, or Crimestoppers, anonymously, on 0800 555 111.