The fire was started by sparks from cutters that were being used to remove wreckage, the BBC said, and four firefighters have been taken to the hospital.
The Rana Plaza factory building collapsed Wednesday, killing at least 377 people.
The owner of the building was arrested earlier Sunday, officials said.
Local minister Jahangir Kabir Nanek said soldiers from the Rapid Action Battalion arrested Mohammed Sohel Rana at the Indian border. He had been in hiding near the land-crossing in Benapole since the garment factory building collapse, the BBC reported.
He joins five other people who have been arrested for their alleged fault in the accident, including three factory owners.
About 3,000 people were believed to have been working in the building at the time of the collapse. Some 600 are still missing.
The factory owners are suspected of ignoring cracks in the building and forcing their staff to work in the eight-story structure, the BBC said.
Municipal engineers allegedly approved the safety of the building the day before it collapsed, though police had ordered the evacuation of the building Tuesday because of the cracks, the BBC reported. The factory owners allegedly ignored the warnings.
Meanwhile, rescuers said they pulled four more people from the rubble alive Sunday, CNN reported. They said they've found another nine trapped survivors and hope to free them using light equipment before engineers begin using large cranes and other equipment, the BBC reported.