Rahima Bibi (30), her one-year-old son, Mithu Ali (28) and her 6-month-old baby were burnt to death when they were sleeping in their thatched house.
Seven other family suffered serious burn injuries and they were admitted to the Midnapore district hospital in a critical condition.
Police said they were investigating a complaint of the villagers that Taher Ali, son-in-law of the family, had set the house on fire as he was not allowed to marry his wife Rahima Bibi's sister.