The fire broke out at the Smart Garment Export factory around 2 p.m. Saturday and was controlled in about two hours, BDNews24.com reported.
Among the dead were a doctor and an assistant caring for the injured at the scene, and five factory workers, officials said.
"Doctors at the Sikder Medical College declared five female workers of the factory dead after they were rushed there in a critical condition," Mohammadpur Police spokesman Azizul Haque said.
Four other employees of factory, which made sweaters and jackets, were injured.
Fire Department Supervisor DeMasudur Rahman Akand said the workers were returning from lunch when the fire started in a storage area in the factory, The New York Times reported. Officials told BDNews24.com that the fire may have started in a boiler room.
Workers said their supervisors locked one of the factory exits, forcing some of them to jump out of windows, The Times said
Akand said the dead either suffocated or were trampled by others trying to escape.
The factory, which was located on the second floor of a building, lacked proper ventilation and fire prevention equipment, Akand said.
"We did not find fire extinguishers," he said. "We did not find any safety measures."
The latest fire came in the wake of a Nov. 24 fire at Bangladesh's Tazreen Fashions factory that killed 110 employees and left more than 200 injured.