Officers said 13 men had been arrested in West Bengal state after the incident.
A series of rapes in India over the past year has sparked widespread outrage over chronic sexual violence in India and government failures to protect women.
The West Bengal case is particularly troubling because the alleged rape apparently was sanctioned by a council made up of village elders.
Such councils are not legally binding in India but they are seen as the will of the local community and those who flout the councils risk being ostracised.
The woman told police the village council in Subalpur ordered her to pay a fine for having an affair with the man but, when her family said they were too poor to pay, the council ordered the gang rape.
The woman told police she lost count of how many men raped her during the night-long ordeal. She is in hospital in the state's Birbhum district where doctors said her condition is serious.