"We agree that this is a serious matter and that we have not lived up to what our customers should rightfully expect of us," Chief Executive Chris Vogelzang said in a statement.
Denmark's financial watchdog reported Danske Bank to the police in August.
It said the bank had failed to inform customers that it expected a poor performance from its Flexinvest Fri investment product and for continuing to sell it to new customers after raising fees associated with it in 2017.
(Reporting by Jacob Gronholt-Pedersen; editing by Jason Neely)