The cause of the blaze wasn't immediately known, fire service director Tajul Islam Chowdhury said.
"Sixteen bodies have been recovered from the second and third floors of the garment factory," he said.
The fire broke out on the third floor of the four-storey factory in the Mirpur area of the capital Dhaka, before spreading to a chemical warehouse storing bleaching powder, plastic and hydrogen peroxide, Talha Bin Jashim, a fire department official said, citing witnesses.
Firefighters brought the factory blaze under control after nearly three hours, though the fire at the warehouse continued.
Grief-stricken relatives gathered to search for their loved ones, some clutching photographs.
In front of the blackened ruins, a father searched desperately for his daughter, Farzana Akhter.
"My daughter worked there. When I heard about the fire, I came running. But I still haven't found her....I just want my daughter back."
Chowdhury said the owners of the factory had not yet been identified.
"The police and the army are trying to locate them," he said.
He added that neither the garment factory nor the chemical warehouse had approval or any fire safety plan.
Based on the initial findings, he said the garment factory had a tin roof with a grilled door that was kept locked.
"The workers couldn't reach the upper level," he said
"The chemical explosion caused a flashover that released toxic gas, leaving many unconscious and trapping them inside. They couldn't escape either upward or downward."
He said the victims were so badly burned, DNA testing may be the only way to identify them.
In a condolence message, Bangladesh's interim government head Muhammad Yunus expressed deep sorrow and urged authorities to investigate and support victims and families.
Poor fire and building safety standards lead to dozens of such disasters in Bangladesh each year, and past accidents have tarnished the country's garments sector, which employs four million people and makes up more than 10 per cent of the country's GDP.
In 2012, a fire at Tazreen Fashions that supplied global brands, killed 112 workers.
A year later, the eight-storey Rana Plaza building collapsed, killing 1135 garment workers and triggering a wave of public outrage around the world about the human cost of cheap clothes.
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