Bishop Bernt Eidsvig (left) with unconnected colleague - Catholic Church of Norway
The 31-year-old, who has confessed to a relationship with the girl which lasted a little over a week, allegedly consummated it at the rectory where he lived in the city of Bergen.
"He met for questioning and there acknowledged the facts," Rigmor Isehaug of the Hordaland police said on Tuesday.
The Catholic Church disclosed the abuse in a press release on August 20, just two weeks after Bernt Eidsvig, the bishop of Oslo, learned of what had happened.
He sought to play down the event, saying that the priest, who is not Norwegian, was "distraught" over the relationship which took place over "a short period" this summer.
The case will now go for prosecution.