Al Jazeera's Nicolas Haque, reporting from the scene, described it as "chaotic".
He said the army and police had been called in to manage a crowd gathered at the base of the tower that was hampering the firefighters.
"Firefighters haven't managed to come near the flames," he reported. "They've climbed on an adjoining building, but are nowhere near control.
"They simply don't have the equipment to fight such a massive fire. The building was built just five years ago, but unfortunately there were no fire systems put inside."
Haque reported that people were still trapped inside the building as it continued to blaze into the night.
Friday is a holiday in Bangladesh, and the shopping centre was packed with hundreds of shoppers.
Security staff from the complex said the fire started in the building's corporate offices on the two top floors, which are usually closed on Friday.
The cause of the fire is not immediately known.
The shopping centre, which opened in 2004, was the first Western-style complex to operate in Bangladesh, and contained around 2,000 shops.