Dozens of workers were inside the factory on the outskirts of Dhaka when the boiler exploded on Monday evening, causing a section of the six-storey building to collapse.
It was unclear what caused the explosion, which occurred during maintenance work on the boiler at a time when most workers were off for the Eid holidays.
"We were meant to open the factory today after the Eid holiday so we were checking the equipment yesterday," said operations director Mesba Faruqui.
The government said it had formed a committee to investigate the explosion, the latest disaster to hit the country's $30-billion garment industry.
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The plant in the Gazipur industrial district is owned by manufacturer Multifabs, which makes clothing for brands including Littlewoods and Aldi according to its website.
The collapse of the nine-storey Rana Plaza factory complex in April 2013 in which than 1,100 people were killed was seen as a wake-up call for the industry, which supplies clothing for major brands all over the world.
In the wake of the disaster, authorities pledged to improve working conditions at factories but accidents are still commonplace.
A survey this year by global charity Action Aid of more than 1,400 Rana Plana survivors found nearly half were still jobless while roughly 31 percent were too traumatised to work.
There have also been demands for an increase in the basic monthly wage of $68 for the country's four million garment workers, most of whom are women.
Three workers remain unaccounted for after the latest disaster, and district administrator Mahmud Hasan said the toll could rise further.