Police say the men took turns to assault the victim and film it.
The woman was reportedly dragged from the Ganges, where she had been bathing on Sunday morning.
In the video, she can be heard asking the men to consider the "sanctity" of the river, revered within Hinduism.
She also refers to it as "mother" - a term of affection and respect for the site.
Police said on Wednesday the mobile phone used to film the alleged assault had been seized and would be sent to a forensic laboratory for analysis, the Times of India reports.