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The woman, who is now recovering in hospital, told police she was assaulted by the men on the night of Jan. 20 in Birbhum district in West Bengal.
Police said that her male companion was tied up in the village square, while the assault on the woman happened in a mud house.
"We arrested all the 13 men, including the village chief who ordered the gang rape. The accused have been produced in court which remanded them to jail custody," Birbhum's Superintendent of Police, C. Sudhakar, told the Thomson Reuters Foundation.
India toughened laws on sex crimes in March last year following the fatal gang rape of a physiotherapist on a moving bus in Delhi in December 2012. The case led to nationwide protests for better security and has helped sparked national debate about gender inequalities in India.
The issue was highlighted in local media again last week after a 51-year-old Danish tourist was gang-raped in central Delhi by at least five men whom she had asked for directions.
The West Bengal victim's family told media that she was assaulted because the court believed she had violated the rules of her tribe by falling in love with a man from another community.
The couple were ordered to pay a fine of 25,000 rupees ($400), said the victim's mother, adding that the village head then ordered the rape of her daughter.
Human rights groups say diktats issued by kangaroo courts are not uncommon in rural regions.
In northern parts of India, illegal village councils known as "Khap Panchayats" act as de-facto courts settling rural disputes on everything from land and cattle to matrimony and murder.
But such councils are coming under growing scrutiny as their punitive edicts grow more regressive - ranging from banning women from wearing western clothing and using mobile phones to supporting child marriage and sanctioning the lynching of young couples in so-called "honour killings".
The assault comes after a spate of high profile rapes in West Bengal which have brought Chief Minister Mamta Banerjee under fire for not doing enough to stop violence against women.
West Bengal recorded the highest number of gender crimes in the country at 30,942 in 2012 - 12.7 percent of India's total recorded crimes against women. These crimes include rape, kidnapping and sexual harassment and molestation.
Earlier this month, West Bengal's capital, Kolkata, witnessed public protests against police who have been accused of failing to act on the gang rape of a 16-year-old girl who was later murdered.