The 21-year-old woman was fatally attacked late Wednesday by her father, after he found her alone at her in-laws house in Buldhana district of Maharashtra state.
She and her husband and been staying with his family in Nimkheda village, after they secretly married in March.
Woman stabbed to death ‘by in-laws’ for honour in Lahore
The husband found the young woman lying in a pool of blood and rushed her to a hospital, where she was pronounced dead.
"He [the father] came to the police station and admitted killing his daughter with an axe. We have arrested him," Baburao Mahamuni, deputy police chief for Buldhana said.
"The accused told us that he had fixed her marriage with a man but she eloped with her lover who belongs to a different caste," the officer added.
Many parents deem unions from outside their castes as an insult to their clan. But killings can also be prompted by relationships within the same "gotra" - or kinship group - that are considered incestuous despite the lack of genetic links.
With his own hands: Man strangles daughter for ‘honour’
Last month a man slit his 15-year-old daughter's throat after she was caught dating a teenager from the same caste in northern Uttar Pradesh state.
So-called honour killings have been carried out for centuries in the country, especially in rural areas.
They are typically enacted by close relatives or village elders to protect what is seen as the family's reputation in a rigid caste system.
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.
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