The expenses involved chauffeur costs and wine storage fees.
ANZ New Zealand chairman Sir John Key said Hisco's departure was the right in the circumstances "given the expectations we have of all our people, no matter how senior or junior".
Early this month, McDonald called on Key and other ANZ directors to resign after the bank was censured by the Reserve Bank for failing to properly calculate its risk.
The Reserve Bank had ordered ANZ to increase how much capital it holds as a safety net to absorb possible losses and said its model for calculating its risk had failed over five years.
In addition, ANZ and the other big banks have staunchly resisted a Reserve Bank proposal for them to lift their minimum capital requirements.
McDonald has been critical of all the banks but singled out ANZ for its failings and took aim at the Reserve Bank for not acting more decisively over the breach.
He said today's announcement involving the chief executive of New Zealand's biggest bank was serious.
"That the head of New Zealand's biggest bank should have done this really does raise serious issues about governance of the bank," he said.
"It's another failure by the bank," he said.
"I have focused particularly on the chairman [Key] because the chairman leads the board, but I was also very clear that the board overall needs to be refreshed and, to me, that will take at least two additional resignations," he said.
"Having to dismiss your CEO for behaviour of this nature is a very serious event for a bank," he said.
McDonald said he initially opposed a New Zealand commission of inquiry into banking here but changed his mind when results of the inquiry were released.
"Now, with the number of issues around the New Zealand banks, I think it's getting to the time when the Government needs to very seriously consider a royal commission.
"If the regulators continue, in my view, to be ineffective, that will underline the need for a very substantial inquiry and a royal commission would in my view be justified," McDonald said.
Sam Stubbs, chief executive of fund manager Simplicity and a former banker, also called for formal commission of inquiry.
He warned that our politicians were at risk of leaving it too long to act.
"The Prime Minister in Australia ended up apologising to the public for the delay in calling a Royal Commission," said Stubbs, who has also been highly critical of ANZ for its capital breach.
"Jacinda Ardern will have to be looking at this," Stubbs said. "The evidence is mounting up. You've got the chief executive of our biggest bank using shareholder funds for wine storage. Really?"
McDonald, a former chief executive of Comalco, has served on several of New Zealand's biggest companies and is a former president of the New Zealand Institute of Directors.
