A mob of men forced two women to walk naked in India's northeastern state of Manipur, with the footage on social media sparking outrage in the world's most populous country.
The women were then raped.
The police announced that they have opened a case of gang rape and have arrested a man, adding that they will find others soon.
Prime Minister Narendra Modi said the incident had "shamed India" and that "no culprit will be spared".
"I assure the nation, we will resolutely apply the law. What happened to the women of Manipur can never be forgiven," he said.
Violence has been going on in this Indian state for more than two months.
At least 130 have been killed and 60.000 displaced since ethnic clashes between the Meitei and Kuki communities broke out in Manipur in May.
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The Supreme Court also expressed concern over the case and asked the government to take action.
Police say the attack on the women took place on May 4, but became headline news on July 19 after the footage went viral on social media.
The federal government has asked all social networks to delete the video from their platforms.
A terrible video of these two women and the violence against them is circulating on social networks.
It shows a group of men dragging and groping two women and then forcing them into a field.
The Indigenous Tribal Leaders Forum (ITLF) states in the statement that the crime was committed in a village in Kangpokpi district against women from the Kuki-Zo tribal community.
It is also claimed that the women were gang-raped.
'This should not be happening in today's India'
Geeta Pandey, BBC News, Delhi
It is well known that women's bodies often become a battlefield during riots and conflicts, and rape and sexual assault are used as instruments of violence to punish them.
The sexual assault of a mother and daughter from the community, who were stripped of their clothes and made to walk around naked while groped and molested by a mob of men in Manipur, is the latest example of this.
The video showing the women crying, sobbing in pain and begging the attackers to show some mercy is disturbing to watch.
The fact that the first arrest was made only after general outrage in a case that happened 78 days ago and was reported to the police more than two months ago does not inspire much confidence in the authorities - especially since many of the men are clearly recognizable in the video.
But the mass outrage that followed the video's release in India helped bring this horrific crime into the spotlight.
It raised questions about the state's failure to comfort survivors - and finally forced Modi to issue a statement on ethnic violence.
To regain some kind of confidence among the violence-torn people of Manipur, especially the minority Kuki community, the authorities must now act swiftly against the perpetrators of the horrific attack and bring justice to the women.
This should not be happening in today's India.
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