Father David Taylor, who was attached to the Sisters of Mercy Mission in Seaham Harbour from 1981 to 1989, was arrested by Durham Police on 3 May.
He was removed from his post at St Peter's Church, in Low Fell, Gateshead, in March by the Catholic diocese.
Police said the allegation was "historic."
Father Taylor has been bailed pending further inquiries.
A spokesman for Durham Police said: "We can confirm that a 59-year-old Roman Catholic priest was arrested by Seaham Police in connection with an historic allegation of child abuse dating back to the 1980s.
"He has been bailed pending further inquiries and suspended from his diocese."
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