Asha Ram hit daughter Soniya (19) with an axe when she was in sleep in the pre-dawn hours, they said.
Senior Superintendent of Police Deepak Kumar Singh said Soniya was in a relationship with one Gaurav and Ram was not happy with it.
Ram, a tailor by profession, took the extreme step when his wife Rekha went to fetch milk from a nearby dairy and entered into the room where Soniya was sleeping along with her younger sisters. He hit her neck with the sharp-edged weapon.
The body has been sent for postmortem and Ram to jail, the SSP added.