The blaze ravaged the bank’s IT offices before it was brought fully under control at 2.30am, five hours after the alarm sounded.
“When we arrive there was a fully developed fire on the fourth floor,” said fire service spokesman Tomas Lundén.
A total of 55 fire workers were called in to put out the blaze.
There is not believed to have been anybody working at the time and there have so far been no reports of any injuries.
The fire at Swedbank’s IT department did not have an adverse effect on its internet banking system.
“We have reserve systems that take over if anything happens with the network,” said Swedbank’s security chief Bertil Elvén.