Fire Service Control Room official Brojen Sarkar said that the fire was put off by locals.
The injured have been admitted to the Burn Unit of the Dhaka Medical College and Hospital (DMCH).
They are Rahima Begum, 50, her daughters Salma Begum, 30, Sonya Akter, 14 and sons Md Rocky, 27 and Md Akash, 12.
DMCH police outpost's inspector Mozammel Haque said they were brought in around 6.30 am.
Burn unit's resident physician Partha Shankar Paul said Rahima Begum suffered 90 percent burns while others suffered burns between 17 and 35 percent.