In a memo to staff, ANZ said Hisco had taken the decision to step away from his role for an extended period due to health concerns. He is expected to return to the job eventually.
Antonia Watson, retail and business banking head, takes over as acting ANZ New Zealand CEO, according to reports.
ANZ group CEO Shayne Elliott has asked Watson to fill in for Hisco on group meetings.
Watson said: "David has told me he's keen to get back to work as soon as possible but realises how important his health is. We obviously all wish David a speedy recovery."
The board room changes come at a difficult time for ANZ. The bank was censured by the Reserve Bank earlier this month for failing to oversee its internal capital ratio modelling controls. The bank had used an outdated model since 2014.
Because of the oversight, RBNZ revoked ANZ's license to model its own capital, a move that will force the lender to hold $277 million in extra capital for financial stability. ANZ alerted the Reserve Bank to its own failings just last month.