In the video, a woman constable could be seen repeatedly striking the student and berating her for allegedly conducting an interfaith relationship.
“You prefer Muslims when there are so many Hindus around,” a policeman is heard saying in the video clip.
The woman constable also removes the scarf the woman had used to cover her face.
Indian media said the incident took place on Sunday in Uttar Pradesh state’s Meerut city, located on the outskirts of capital, New Delhi.
The woman and her Muslim friend, both medical students in their twenties, were handed over to the police by members of the far-right Vishwa Hindu Parishad (VHP), local media reported.
Police said the female constable and two other police officials have been suspended and an inquiry ordered into the incident.
“Their conduct has led to embarrassment for the UP police,” a senior police official who did not want to be named, told AFP news agency.
“Such behaviour shall never be tolerated,” the Uttar Pradesh police wrote on Twitter amid outrage over the incident.
Before they were handed over to the police, the VHP men had reportedly barged into the man’s house, accusing him of conducting “love jihad” – a term used by Hindu groups to claim that Muslim men attempted to lure Hindu women into marriage in order to convert them.
“People can’t be allowed to do anything in society even if the apex court allows adults to choose their partners,” VHP leader Manish Kumar, who allegedly led the assault on the couple, told Indian newspaper, The Hindustan Times.
The couple was released since there was no complaint from any of their family members about their relationship, local media reports said.
Interfaith relationships are frowned upon in Hindu-majority India, where Muslims constitute about one-fifth of the population.
Rights activists and feminists have accused state institutions of perpetuating a “patriarchal and Islamophobic” narrative pushed by far-right Hindu groups.
In June, an interfaith couple was harassed by an Indian passport official, spurring massive outrage.
Months before that incident, India’s Supreme Court had upheld a controversial marriage between a Muslim man and a Hindu girl, who had converted to Islam before tying the knot.
The federal National Investigation Agency had argued during in court that the marriage, which made national headlines for months, was an example of “love jihad”.
But the court, in its ruling, underlined an adult’s right to marry by choice.