Bank workers don't take strike action lightly, but the bank's proposals had prompted a strong reaction from staff, Ms Gay said.
"ANZ workers want jobs that they can plan their lives around, and they want a pay offer that respects their hard work that delivers such big profits, $1.37 billion last year, for the bank.
"ANZ needs to show some respect and decency towards its workers by offering a pay increase that values the contribution they make and that is significantly greater than the current 2 per cent to 3 per cent offer, and it needs to pull back on its proposal to casualise hours of work."
Ms Gay said the union was working on the details of when the strike will happen, but said "its a little way off" at this stage.
Chief executive of ANZ New Zealand David Hisco earned $4.1 million last year. He was the highest paid chief executive in the country according to a Herald pay survey.
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General banking staff earn between $34,612 and $79,139 per year.
A spokesman for ANZ said branches would be open and customers would be able to make transactions despite the strike.
A statement from ANZ said the proposal of flexible rosters would not casualise jobs or reduce job security.
"We're disappointed that union members have voted for industrial action when a very good offer is on the table," the statement said.
"Staff working on these rosters would have an agreed number of hours that they work each month which cannot be changed without their agreement.
"The proposal simply allows for changes to be made, from time to time, to the days and start/finish times of staff who agree to be employed on a roster so we can respond to any changes in customer demand.
"ANZ pays its staff very competitively compared to similar jobs in the market. The salary ranges for almost all jobs covered by this agreement are the highest in the industry.
The average salary of employees on the collective agreement was $59,000, the statement said.
"ANZ has offered staff pay increases of 3 per cent and 2.75 per cent over the next two years.
"In addition, ANZ pays for medical/health insurance for all staff and provides all staff with discounted lending rates.
The statement said there would be little impact on customers when the strike occurred, as the union members made up 20 per cent of ANZ's 8000 employees.