The incident happened under Domkal police station of Murshidabad district.
Police said the victim identified as Pakhi was not liked by her father Ratan because she was a girl.
Pakhi's mother Rupali, who was not at home when the incident happened, informed police when she found her daughter's body after returning home.
Ratan, a drug addict, married Rupali about one-and-a-half years ago and used to torture his wife but its level increased after their daughter was born, police said.