One of the victims was later shifted to Dhaka.
Kumod Chandranath, father of the children and a pharmaceutical sales representative, told UNB that the fire broke out around 8pm at their rented flat in ward No-8 of the municipality.
According to him, the incident occurred when a family member lit a candle in the kitchen.
A sudden loud sound was heard, and the room instantly caught fire.
Hearing screams, three other family members rushed to the kitchen and sustained burns while trying to rescue each other, he said.
Kumod suspected that accumulated gas in the stove or pipeline ignited, triggering the fire and causing it to spread rapidly. Some household items were also damaged.
Neighbours and locals rushed to the scene, helped evacuate the family, and took them to Companiganj Upazila Health Complex.
Resident Medical Officer Main Uddin said the injured were identified as Edirka, 8, Turya, 4, their father Kumod Chandranath, 43, and mother Savitabani Das, 32.
Of them, Edirka suffered 20 percent burns and was referred to the National Burn and Plastic Surgery Institute in Dhaka, reports UNB.
The others sustained minor injuries, the physician added.