ANZ will close its Fyshwick branch on March 10.
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The bank has blamed a failure to negotiate a new lease for its Wollongong Street site and said it's unrelated to customer activity.
"We've been operating banking services in Fyshwick for a number of years and we're disappointed to be leaving," the bank said in a message to customers.
"Our sincere apologies for any inconvenience this may cause you."
ANZ advised that Fyshwick accounts will be automatically transferred to the Manuka branch 5.4km away on Bougainville Street.
Finance Sector Union national secretary Julia Angrisano said it was a shortsighted decision, which would have an adverse knock-on effect to the local economy.
"There is a trend across all the big banks to review and close branches, not only in rural and regional areas, but in suburbs and cities as well," she said.
"What many people don't realise is that our members have targets to move accounts across to online products."
Ms Angrisano said the union was working with ANZ to ensure Fyshwick staff were redeployed.
An ANZ spokesman said there were five employees at the branch.
"We are fully supporting them through this transition period as we find other ANZ sites for them to work at," she said.
"Our staff members at Fyshwick are working with our customers to help make the transition to our Manuka branch as smooth as possible."
The spokesman said the Fyshwick branch had been operating for more than 20 years.
"We have a long-standing relationship with the local community and our customers and remain committed to providing them with the banking services they need," she said.
"All customers from Fyshwick will be transferred to the Manuka branch, which is less than 6km away.
"Customers can also visit the Woden and Tuggeranong branches nearby. We also have phone and online banking services available to customers 24/7."
An elderly customer, who did not wish to be named, said the bank's closure would be hugely inconvenient.
"I just think it's unfair. A lot of people use this bank and it's going to be tough for them," he said.