Police officers earlier held back the protest group to create a corridor for ANZ staff while the protesters sang: "Standing up for climate, we shall not be moved" just before 9.30am.
One of the protesters was arrested and the ANZ branch was later closed around `10.45am.
About a dozen staff had earlier gathered on a nearby corner as the protesters sung and shouted slogans.
The action was been organised by Climate Liberation Aotearoa which is targeting ANZ branches across the country.
It says other banks have committed to withdrawing banking services from fossil fuel industry but ANZ "is lagging far behind".
An ANZ spokeswoman said the bank supported the right to peaceful protest while prioritising the safety of customers and staff.
"Police were present to support customers entering the branch safely.
"However, after assessing the situation, we made the decision to temporarily close the branch."
ANZ said in a statement its policy was to not lend to "new thermal coal mines, or to expansions, or extensions to the operating life of existing mines.
"And we will not directly finance new coal-fired power plants, including expansions.
"We also don’t provide direct lending to customers who derive more than 10% of their revenue from thermal coal mining or coal-fired generation."
The statement said the bank has been in contact with 350 Aotearoa to explain its position.
