According to reports, the priest, 51, was detained in his home over allegations of abuse in the 1980's.
A woman, now in her 30's, said the church leader was in his late teens when he abused her.
It is understood he has been released on police bail.
A Durham Police spokesperson told Premier Radio: "A 51-year-old man was arrested on Wednesday on suspicion of historical sexual offences. He has been bailed pending further enquiries."
The Diocese of Leeds told Premier: "A 51-year-old priest in the Diocese of Leeds has been suspended by the Bishop following his arrest by Durham Constabulary concerning allegations of historical abuse.
"No further statement will be made at this time."
The vicar has been suspended for the duration of the investigation by the Bishop of Leeds.
