On Friday, the woman’s body was discovered wrapped in plastic and stuffed in a red suitcase near Mathura in the northern state of Uttar Pradesh.
Her father, Nitesh Kumar Yadav, and mother, Brajbala, have not yet made any statements.
The police say they are treating the case as a suspected “honour killing”.
Honour killings – or crimes committed against people who are perceived as breaking age-old traditions – are reported regularly in India.
The victims are mainly young men and women who fall in love or marry against their families’ wishes outside of their caste or within their sub-caste.
In a detailed press release on Monday, police alleged that the 22-year-old’s father murdered her on 17 November after a fight over her marriage with a man from another caste. They alleged that the parents packed the body in a suitcase and left it near the Yamuna expressway at night.
After the body was discovered a day later, a post-mortem was carried out which revealed injury marks on the woman’s head, face and other body parts, police alleged, adding that she died after being “shot twice in the chest”.
They have seized the father’s licensed gun and the car allegedly used in the crime.