"We don't think that it is appropriate that Anthony received a 16 per cent increase," she said.
The rise comes as the average Kiwi worker received a wage rise of 1.9 per cent in the year to September, according to Statistics New Zealand.
But BNZ chairman Doug McKay, BNZ Chairman said Healy's base salary had increased by around 1.9 per cent.
"The total remuneration increase is due to variable incentives based on strong results and deferred incentive payments from previous years falling due."
"Incentive payments are highly variable year-on-year based on performance and can be zero-based on the performance outcome rating determined."
While Healy's pay rose this year ANZ New Zealand chief executive David Hisco and Westpac New Zealand boss David McLean saw slight dips in their pay packages.
Westpac's annual report shows McLean earned A$2.1 million ($2.3m) in the year to September 30, down from A$2.18m last year.
While Hisco received remuneration of A$3.84m in the year to September 30. That was down from A$4.07m in 2016.
ASB bank doesn't release the remuneration figures for its New Zealand chief executive Barbara Chapman.
Williams said even though Hisco and McLean had pay cuts they still remained 50 to 70 times that of the average bank worker, who earned around $50,000 a year.
"That is grotesque."
"Their salaries should be within cooee of their workers."
She called for bank bosses to take a cut.
"It needs to come down, particularly if they want to run around cutting jobs and hours."
BNZ did not respond to the union's comments on Healy's pay.
ANZ said Hisco's salary had remained unchanged since 2014. His remuneration was determined by the board, and comprised both fixed and variable remuneration. Around two-thirds of the total remuneration was variable depending on performance against targets using a balanced scorecard.
A spokesman said salaries for frontline staff had increased cumulatively by 14.8 per cent during the past five years when the CPI had increased 5.1 per cent. They also got other benefits.
A spokeswoman for Westpac said the bank did not want to make any comments around the difference in pay between its chief executive and bank workers.
Banks are coming under increasing pressure to cut staff as customers have moved to do their banking online.
Williams said it discovered on Tuesday that Westpac was proposing to shut five branches - three in Christchurch and one each in Wellington and Auckland, although no job losses were expected.
She said bank staff were being told the closures were all about the move to online but staff were still busy in branches which often meant the change appeared to come from "out of the blue".
"Westpac is to be commended - there aren't going to be job losses. But it is still a shock for people."
The Westpac spokeswoman said the branch closures were still only a proposal at this stage.
"Over the past five years, we have seen the way our customers use our banking facilities change. Online transactions have increased by 66 per cent in the past five years and in the last two years the percentage of customers using mobile-only devices has increased from 24 per cent to 39 per cent.
"At the same time, many of our branches are experiencing a decline in over-the-counter transactions. This is the case for example with five branches in Auckland, Wellington and Christchurch, which we are proposing to consolidate with nearby branches."
She said under the current proposal, if it went ahead, Westpac would be looking to actively transfer the majority of affected staff to nearby branches.
