The fire started on Saturday night at the BM Container Depot in Sitakunda, in Chittagong District, according to state-run news agency Bangladesh Sangbad Sangstha (BSS).
Among the dead are at least nine firefighters who had been deployed to douse the flames, BSS reported. Two firefighters remained missing late on Sunday.
Firefighters were still working to extinguish the blaze on Sunday afternoon, as containers filled with chemicals including hydrogen peroxide or sulphur continued to erupt, Reuters reported, citing fire service officials.
While the cause of the fire remains unknown, fire service officials said it may have originated from a vessel of hydrogen peroxide and diffused to other containers.
"It's really getting harder as toxic fumes engulfed the area," Newton Das, a fire service official, told Reuters.
Local residents told the agency that the initial blast caused the neighborhood to quake, and subsequently broke some of the glass windows on local infrastructure.
The depot's authorities have announced that they would provide 10 lakh Bangladeshi taka (around $11,200) in compensation to each family of the workers who died in the fire, BSS said.
They also promised to pay six lakh Bangladeshi taka (around $6700) to each critically injured worker who lost body parts in the fire and four lakh Bangladeshi taka (around $4500) to other injured workers.
The company has formed a five-member inquiry committee to probe the deadly incident, the state news agency reported.
The incident is the latest in a string of fatal industrial accidents over several years in the South Asian nation.
In December, at least 38 people were killed after a fire destroyed a launch on the Sugandha River, in the southern district of Jhalakathi.
A few months earlier, at least 52 people died and about 50 others were left injured when a huge fire swept through a juice factory in Rupganj, east of the capital Dhaka.