A Catholic bishop in New Zealand has resigned after a church body investigated a young woman's sexual complaint against him, a top church official has said.

Pope Francis accepted the resignation of Bishop Charles Drennan of Palmerston North, Cardinal John Dew, the metropolitan archbishop of New Zealand, said in a statement.

"Bishop Drennan tendered his resignation to Pope Francis following an investigation into a complaint of unacceptable behaviour of a sexual nature," added the statement, posted on the website of the New Zealand Catholic Bishops' Conference.

The New Zealand church's independent investigation body, the National Office of Professional Standards (NOPS), carried out the investigation, it said.

"In the eyes of the Catholic Church, Bishop Drennan's behavior was completely unacceptable, and it fully supports the young woman for coming forward to NOPS," Dew added.

Catholic priests take a vow of celibacy, though the church has been embroiled in a sexual abuse crisis around the world.

Drennan, appointed in 2012 as the bishop of Palmerston North, was born in Christchurch in 1960 and ordained a priest in 1996, his biography on the diocese website shows.

In the statement, Dew said the woman, who wanted the details of her complaint kept private, was told of the resignation and church officials were in contact with her.

"The Catholic Church has no tolerance for any inappropriate behavior by any of its members," the statement cited Dew as saying, adding that he urged anyone who experienced such behavior to notify the church, police or other authorities.