The central bank wants the lender to provide two independent reports, one on compliance with capital adequacy rules, and another on internal governance, risk management and internal controls.
The reviews come at a period of turmoil for ANZ, which was reprimanded last month for using an outdated capital model, and saw its CEO step down last week over a personal expenses scandal.
The Reserve Bank punished ANZ for its capital modelling failings and forced it to adopt a new approach requiring an extra $277 million in risk capital.
While former CEO David Hisco left last week after revelations he had spent tens of thousands of dollars on chauffeur-driven cars and wine cellaring.
ANZ faced further scrutiny this weekend amid reports Hisco's wife bought an Auckland property from the bank at below the market rate.
The reviews are likely to heap further pressure on ANZ chairman Sir John Key, the former prime minister, who has faced calls to resign over the capital blunder and Hisco scandal.
ANZ said it would work with the central bank to provide the independent reports.
In a statement, ANZ said it was "sound and well-capitalised" and has $12.4 billion of capital, nearly $3.5 billion more than its regulatory requirement.
ANZ NZ chairman Key said: "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.
"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," Key added.