About 200 firefighters had battled for more than five hours to contain the blaze in narrow lanes snaking between tightly-packed buildings in an area authorities say is home to more than 3 million people.
Shopowner Haji Abdul Kader told Agence France-Presse he "heard a big bang", and then "saw the whole street in flames".
Fire service control room said that the fire broke out following an explosion at a chemical warehouse housed in a five-storey building at Churihatta around 10:45pm.
Doctors at Dhaka Medical College Hospital said 10 people are in a critical condition.
Numerous city's residents said the fire is reminiscent of a similar tragedy that left 120 people dead in 2010.
Over 50 people, including women and children, were also injured and admitted to nearby hospitals, including Dhaka Medical College Hospital (DMCH) and Sir Salimullah Medical College Hospital.
"Our teams are working there but numerous recovered bodies are beyond recognition. Flames were everywhere", he said.
The centuries-old Chawkbazar district has narrow streets and buildings very close to each other.
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Hundreds of people rushed to the hospital to look for missing relatives.
Most buildings in Chawkbazar are used both for residential and commercial purposes despite warnings of the potential for high fatalities from fires after one killed at least 123 people in 2010.
Dhaka authorities launched a crackdown on chemical warehouses in residential areas following the blaze, but efforts to rein in the practice have waned.
Chemicals were also stored in the nearby buildings which exploded in a chain as the fire spread.
Sohag Hossain, one of the injured, told the Daily Star that he and two friends were working at a plastic factory in one of the buildings at the time of the fire.
Lax regulations and poor enforcement of rules in impoverished Bangladesh have often been blamed for several large fires that have led to hundreds of deaths in recent years.
At least 1,130 people died when Dhaka's Rana Plaza nine-storey factory complex collapsed in April 2013 - one of the world's worst industrial tragedies.
Witnesses told local TV many gas cylinders stored in the buildings continued to explode one after another.
It is not the first time a deadly fire has devastated parts of Dhaka.