Security staff from the complex said the two floors on fire contained the building's corporate offices, which were usually closed on Friday.
Al Jazeera's Tanveer Choudhry, reporting from Dhaka, said that rescue teams were not equipped to save people from the top floors.
"The firefighters don't have that kind of sophisticated equipment to put the ladder up that high," he said.
"Having said that, I am giving the situation the benefit of the doubt because the building is new and it's equipped with fire-safety equipment with sprinklers and fire hoses, a fire escape - all the kind of amenities you would expect inside a shopping centre."
The cause of the fire was not immediately known.
The mall, which opened in 2004 and took six years to build, was the first Western-style shopping mall to operate in Bangladesh.