The blaze began on the 17th floor of the 21-storey Basundhara City complex in the city center, damaging several offices and destroying a furniture store. None of the building's lower offices were damaged.
The complex, which houses 2,000 stores, was opened in 2004 and is visited by around 25,000 people daily.
The cause of the blaze has not yet been determined.
The building was largely empty at the time of the fire, as Friday is not a work day in the Muslim country.
Television stations have been showing people evacuating the engulfed upper floors. Dozens of people are said to be trapped above the 17th floor, many of whom have escaped to the roof to be evacuated by helicopter.
Firefighting work is complicated by strong winds that are fanning the fire through the building, while high temperatures have started to melt the windows.
