ANZ chairman and ex-Prime Minister John Key. - Photo: RNZ / Dan Cook
ANZ is being asked to provide two reports to show it's being run properly and in line with regulations.
The first is on the bank's level of capital reserves and whether it is meeting the required level.
Last month, ANZ was censured and ordered to increase its level of capital and reserves to cover any crisis by hundreds of millions of dollars, because it had been using out of date models to calculate the financial risks it was facing and how much money it needed to cover them.
RBNZ directly blamed the ANZ's local directors for the lapse. Last week, local chair Sir John Key said a junior member of staff made a mistake.
The second report is whether ANZ is complying with rules for the running of the bank by directors and senior staff.
ANZ's local chief executive David Hisco abruptly left the company last week over a dispute on personal expenses which had been charged as company spending.
Sir John said the bank and Mr Hisco had mutually agreed to a parting of the ways over the expenses issue, which had involved tens of thousands of dollars of spending on chauffeur driven cars and wine storage in Australia, and had been represented as company expenses when they were personal costs.
In a statement, ANZ said it welcomed the review.
"The board had been working on commencing an independent review to provide assurance that our capital models and the directors' attestation process are robust and operating in a prudent manner," Sir John said.
"Following discussions with the RBNZ, the directors agree that the best way to achieve this assurance is working with the RBNZ and an independent party to undertake the necessary reviews," he said.
The Reserve Bank is the regulator of the banking sector but generally takes a hands-off approach.
Last year it joined with the Financial Markets Authority to order a review of the culture and conduct of the banking sector to ensure that customers were not being ripped off and deceived as had emerged in Australia's banking royal commission. The review found some grounds for improvement but no evidence of the widespread misconduct seen in Australia.