All the dead were Basundhara employees, one from its fire fighting unit and six were security guards, police said.
One of the dead was a firefighter stationed permanently in the Bashundhara city mall.
"The firefighter died in a hospital where he was admitted with serious burn injuries," a local police officer said.
Doctors at Shamarita hospital said 17 people were being treated there for smoke inhalation. Other hospitals reported receiving at least 33 people.
Mahbubur Rahman, a fire official, said an air force helicopter rescued three people from the roof of the tower.
Hundreds of shoppers fled the building as flames shot into the air.
Al Jazeera's Nicolas Haque, reporting from the street below, described the scene 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.
"The firefighters simply don't have the equipment to fight such a massive fire," he reported.
Security staff from the complex said the fire started in the building's corporate offices on the two top floors, which were empty at the time. Friday is a holiday in Bangladesh.
The inferno has raised questions about the efficiency of fire fighters and whether the high-rise buildings followed required safety measures, Tanzim Ahmed Sohel Taj, the state minister for home affairs, said.
"We will look at these issues quickly after the current disaster has been tackled."
A Basundhara official said the exact death toll and the extent of damage would not be known until the debris was cleared.
The cause of the fire was not immediately known.
The shopping centre, which opened in 2004, was the first Western-style complex to operate in the country, with around 2,000 shops and cafes.