Seriously injured Nunu, an elected Ssarpanch (headwoman) of the village, was admitted to a hospital.
Deputy Superintendent of Police Ashok Kumar Singh said five people have been booked for the crime. All the accused were on the run, he said.
According to the police, some villagers blamed the woman for the illness of two people and said she practiced witchcraft.
They asked her to cure the two. When she said she could not do it, they attacked her with bomboo and iron sticks.
Later, they chopped a part of her nose with a sharp weapon.
The practice of branding women as witches and torturing them - often to death - continues unabated in rural Bihar.
Some months ago, a woman in Sitamarhi district was forced to eat human excreta after villagers branded her a witch.
Last year, the Bihar Human Rights Commission had directed the government to expedite probe and trial in cases related to offences under the Prevention of Witch Hunting Act, 1999.