The white-bearded guru has dismissed the claims against him as a political conspiracy.
The alleged attack took place on August 15 as Asaram was holding a retreat for followers, including the girl and her parents, police said.
He told the parents he needed to meet their daughter alone after being told of concerns she was possessed by evil spirits, police said.
Once alone in his room, the guru allegedly sexually assaulted the girl, who told her parents two days later.
The family then sought to confront him but the guru refused to meet them, prompting them to go to the police.
Asaram sparked an angry reaction in January when he said a 23-year-old woman could have avoided being brutally gang-raped on a moving bus in New Delhi by begging for mercy from her attackers.
The student later died from horrific injuries that she received in the attack last December.
Asaram has some 350 ashrams or religious retreats in India and overseas, where he teaches yoga, meditation and offers lessons on leading a spiritual and peaceful existence, according to his website.
For many Indians, "godmen" play an integral role in daily life. They say they offer them a pathway to enlightenment in return for spiritual devotion and often hefty donations to their ashrams, temples and charity projects.
- AAP