The action came on the heels of the group's 36-hour protest blocking Norway's largest oil refinery on its southwestern coast.
"There are more than 100 activists outside DNB's flagship bank on the main Karl Johan avenue," Oslo police operations leader Anders Aas told AFP just after 12:15 pm (1015 GMT), adding that police were monitoring the situation at the scene.
"Sixteen of them entered the bank but were asked to leave," he said.
No arrests had been made.
The protest was organised by Extinction Rebellion.
In a statement, the Reclaim the Future organisation which was also taking part in the protest claimed DNB was "the bank in Scandinavia investing the most money in the expanding fossil fuel industry."
It said the demonstrators inside the bank unfurled banners, chanted and made speeches demanding Norway phase out its oil and gas business.
"We have come here from across Europe to shed light on the violence that the fossil fuel industry is committing everyday against all life," 23-year-old activist Rufus Rune from Sweden said in the statement.
"First we conducted Norway's biggest blockade against fossil fuel infrastructure, now we're focusing on the financial institutions that enable their deadly operations."
Norway, western Europe's biggest oil and gas producer, is regularly criticised for its huge fossil fuel output.
Oslo insists its industry provides jobs and develops know-how, and stresses the importance of guaranteeing stable energy deliveries to Europe.
Equinor, which owns the Mongstad refinery and is itself majority-owned by the Norwegian state, has said it intends to keep its oil production in the country stable at 1.2 million barrels per day until 2035, and expects to produce 40 billion cubic metres of gas a year by 2035.
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