ANZ plans to cut 23 workers from its Auckland offices and outsource the work to India.
The bank, which also confirmed 70 job cuts in Australia today, said the move was part of an efficiency drive.
"We are always looking at ways to make the business more efficient while not compromising customer service. It makes sense to play to each country's strengths for some bank functions," said a spokesman for the bank.
He said ANZ routinely deployed skills and responsibility to other parts of the business where they were needed or where there was expertise.
"Some countries have a particular strength when it comes to a particular skill or delivering the best service."
The bank said it was looking at moving responsibility for 23 lending services roles to Bangalore. None of the roles were front office.
It was also looking at jobs that it could bring back to New Zealand.
First Union general secretary Robert Reid said sending the jobs offshore was completely unnecessary given the profitability of the bank.
Last year ANZ's New Zealand arm made a record statutory profit of $1.26 billion - up 17 per cent on the previous year.
"This is a bank that does very well off New Zealanders, and it should repay some of that custom by committing to keeping jobs in New Zealand," said Reid.
Reid said the union was also closely monitoring any staffing changes as a result of the closure of the National Bank, following bank commitments last year that staff wouldn't be losing their jobs as National Bank operations are folded into ANZ.