The infant was being breast-fed by her mother when the animal attacked her yesterday, they added.
The child was taken to the AIIMS Trauma Centre, where she died during treatment.
The police have registered a case and are trying to ascertain the identity of the owner of the animal.
The infant was called Pushpa by her family members but it was not her formal name.
Her mother Puja told the police that the pig came inside their house and bit the child on the head.
The incident came to light after one of the neighbours, Raju, informed the police.
The infant's family is in a state of shock. They do not even have a photograph of the girl.