Burdwan district superintendent of police S M H Mirza said the mother was allegedly helped by the baby's paternal uncle with whom she was in an illegal relation.
The baby's father was not at home at the time.
The baby was then taken to a nearby hospital by the mother who told the doctors that she had gone still suddenly.
The baby's father who was informed of her death rushed home and suspecting his wife complained to the police, Mirza said.
The uncle is absconding, he added.