Video footage showed flames spreading across all of the Samhwan Art Nouveau commercial and residential building.
Hundreds of people were reportedly evacuated, including from the roof, the Yonhap news agency said, with dozens suffering smoke inhalation.
The blaze reportedly started at about 23:00 local time (14:00 GMT) and was spread by high winds.
It is now reported to have been extinguished.
The fire broke out between the 8th and 12th floors of the building, which has about 120 households and shopping units.
