At least 50 people were also injured when fierce fire engulfed packaging factory north of the capital Dhaka.
About 100 people are believed to have been working at the building when flames tore through the four-storey factory.
A series of deadly incidents have raised concern over safety standards in the South Asian country’s factories.
"What I have seen here is an industry with bad safety provisions," Shaidul Haq, the inspector general of Bangladesh police told reporters gathered in the capital.
"We have to look into whether the factory had proper permission or proper documents."
Working conditions have been described as notoriously poor, with little enforcement of safety laws, while overcrowding and locked fire doors are common.
A fire at a plastics factory last year killed 13, and in 2013 more than 1,100 people died in the Rana Plaza factory collapse, Bangladesh’s worst industrial accident.
- A series of deadly incidents at Bangladeshi factories, including the 2013 Rana Plaza collapse, have raised alarm