The girl's father slit her throat and dumped the 15-year-old's body on the doorstep of her boyfriend's house in the Muzaffarnagar district of Uttar Pradesh state, local police officer Shivraj Singh told AFP.
"We have arrested the father for her murder," he said.
The boyfriend allegedly sneaked into the girl's house early Tuesday but was caught by her mother and handed over to police, Singh said.
Her father, learning about the incident, returned home and butchered his daughter with a meat cleaver before leaving her body at the teenager's home.
Both their Muslim families had disapproved of the relationship because the teenagers came from the same caste.
Some Indians perceive unions from the same "gotra" -- or kinship group -- as incestuous despite the lack of genetic links.
Strong beliefs around same-caste pairings have been a motivating factor in many so-called honour killings across India, as have inter-faith relationships.
On Tuesday a teenage couple allegedly committed suicide in neighbouring Shahjahanpur district after coming under immense pressure as they followed different faiths.
"Honour" killings have been carried out for centuries in India, especially in rural areas, where close relatives or village elders seek to restore their family's honour after a perceived transgression.
United Nations statistics suggest 1,000 of the 5,000 such murders globally every year occur in India.
The Supreme Court ruled in 2011 that those found guilty of such killings should face the death penalty.
