The fire originated in a restaurant and quickly spread to other floors, fire service officials said.
At least 43 people have died and 22 others are being treated at hospitals with burn wounds, Health Minister Samanta Lal Sen told reporters after visiting the Dhaka Medical College Hospital.
All 22 people admitted with severe burns are in critical condition, Sen added.
It was not immediately clear what caused the blaze, which was under control after two hours of frantic efforts by 13 firefighting units.
Survivor Mohammad Altaf, speaking to reporters, recounted narrowly escaping the blaze through a broken window. Two of his coworkers perished, he said.
"When the fire started in the front and broke the glass, our cashier and servicemen got everyone out. But both of them died later. I went to the kitchen, broke a window and jumped to save myself," Altaf said.
Firefighters used a crane to rescue people from the charred building.
Bangladesh Fire Service and Civil Defence Director, Brigadier General Main Uddin, said the fire could have originated from a gas leak or stove.
"It was a dangerous building with gas cylinders on every floor, even on the staircases," he told reporters.
Intense scrutiny of Bangladesh and the major international clothing retailers that manufacture in the country has helped prevent further disasters in the garment sector since a fire in 2012 and a building collapse in 2013 together killed more than 1,200 workers.
But in other industries, mainly catering to Bangladesh's booming domestic economy and without an equal emphasis on safety, hundreds have died in fires in recent years.
Fires are common in densely populated Dhaka, which has experienced a boom in new buildings, often constructed without proper safety measures. Fires and explosions have occurred due to faulty gas cylinders, air conditioners and bad electrical wiring.
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