The tragedy struck around 8:30pm on Friday at Kumartek under Sector 11 of Purbachal Uposhahar.
The victims have been identified as Md Masum, 40, his wife Sima Begum, 32, and their sons Md Russell, 17, and Rahmat Ullah, 10. Sima also has disabilities.
A torn electric wire of Dhaka Electric Supply Company or DESCO fell on a power line of Rural Electrification Board in the evening, said Uddipan Bhakta, station officer of Purbachal Fire Service.
After sparks, the REB cable fell on the tin-shed house of the victims, triggering the fire. Masum and the two boys died at once while Sima was declared dead at the Rupganj Upazila Health Complex, said Uddipan.
The fire service official said the firefighters doused the fire immediately as the house is situated very near the station.
The bodies were sent to the Narayanganj General Hospital mortuary for post-mortem examination, said Rupganj Police Station OC Mohsinul Quader.