Concerns about Bishop Kavanagh were referred to the Vatican late last year under a decree issued by Pope Francis in May 2019.
The decree requires the Metropolitan Archbishop of a country to inquire into, and report to Rome, any serious allegations against a bishop.
The Otago Daily Times previously revealed the actions of a former Catholic priest, Magnus Murray, who offended against boys in Dunedin from the 1950s to the 1970s, were brought to Bishop Kavanagh's attention in 1972.
Bishop Kavanagh moved Murray to Australia, and later allowed him to resume public ministry in the North Island, where more victims have since emerged.
Metropolitan Archbishop of New Zealand Cardinal John Dew yesterday said he was told the complaints did not fall within Rome's scope because Bishop Kavanagh was dead.
(He died in 1985).
Cardinal Dew had therefore instructed the church's complaints body, the National Office for Professional Standards (NOPS), to undertake an investigation, which will be led by Christchurch senior investigator Micky Earl, of the firm Corporate Risks.
The investigation would focus on understanding what information Bishop Kavanagh had held regarding complaints of sexual abuse, and whether he met his obligations as bishop in how he responded to and managed those complaints, Cardinal Dew said.
Recommendations will be made to Cardinal Dew, who said they could help form the basis of any decision to rename Kavanagh College.
Abuse survivors, their supporters and a group of former pupils have called for the
name to be changed.
Kavanagh College Board of Trustees chairwoman Barb Long declined to comment when contacted last night, saying the investigation was independent and the school was not part of it.
Cardinal Dew encouraged anyone who had any concerns regarding inappropriate behaviour in a Catholic Church setting to contact NOPS.
"We are committed to a safe environment for all within the church community. Any form of misconduct or inappropriate behaviour in the church community is not acceptable."
Meanwhile, survivors of abuse in faith-based institutions are preparing to give evidence at hearings as part of the royal commission.
The first hearing will begin on November 30.