"We are sending a clear message that this is unacceptable," Sasja Beslik, head of responsible investments at Stockholm-based Nordea, told AFP.
"We believe this action, or lack of action, from the management is outrageous. It's poor judgment in terms of business, but it's also very costly from a financial point of view," he said.
Volkswagen, the world's biggest carmaker by sales, admitted on Tuesday that as many as 11 million of its diesel cars worldwide are equipped with software capable of fooling official pollution tests.
Nordea, which said it holds around two billion kronor (2.1 billion euros, $2.4 billion) worth of VW shares and bonds, said however it would not sell off its stake.
"We won't sell our holdings because they are our way to engage with the management. And we could join a class action," Beslik said.
"We evaluate all investments from both financial, environmental and social perspectives. This is a textbook case of how to not behave credibly and honestly," he told Swedish financial daily Dagens Industri.
While Nordea as a shareholder was scathing in its criticism of VW, it was more measured in its forecast of the effect of the scandal on the German economy.
"I have a very hard time seeing that the scandal will hit the economy as whole," Nordea economist Holger Sandte tweeted.
Nordea, the only so-called systemic bank in the Nordic region, manages around two billion euros of assets worldwide.