Videos posted on social media by witnesses showed parts of the building on fire with the flames spreading to at least three floors.
The fire which started early in the morning has been brought under control by officials of the fire service, the bank said in a statement on Twitter.
According to the bank, there was no casualty or loss of lives in the fire and observations as of 8:48 am showed that it did not affect the banking hall or “other strategic business areas”.
The cause of the fire has yet to be identified.
Several people have expressed solidarity and support for the bank, which is listed on the Nigerian Stock Exchange and has more than 200 branches across the 36 states of the country and the FCT.
The bank on its part thanked the agencies and volunteers that helped battle the fire. (Channels TV)