"We have arrested the Baba under Section 376 (rape) and section 506 (criminal intimidation)," Rahul Prakash, Superintendent of Police Alwar, told IANS on phone.
He said that Falahari Baba would be taken to a government hospital for a medical check and later if he is found fit and healthy he would be presented before a magistrate.
The young woman from Chhattisgarh alleged she had been raped by the 70-year-old godman at his ashram in Alwar in Rajasthan on 7 August.
Her family has been the Baba's follower for over 15 years and claimed to have given large donations to the godman.
Facing sexual assault accusations, the Baba got himself admitted in the Intensive Care Unit (ICU) of a private hospital in Alwar on Wednesday under police security.
On Friday, doctors at the hospital found him fit and he was shifted to a private ward.
The Baba has followers both in India and abroad.
"We have already recorded the statement of the young woman and have taken her to the ashram to identify the room where the crime occurred, and the Baba's disciple who dropped her at the Alwar railway station thereafter on 21 September," a police official said.
Police has sealed the godman's room, in front of which he would sit on a throne and deliver his sermon to followers.
A FIR was filed by the woman at Bilaspur in Chhattisgarh, which was transferred to Alwar's Aravali Vihar police station.
The case comes in the wake of the conviction of Sirsa-based Dera Sacha Sauda chief Gurmeet Ram Rahim Singh by a Panchkula special court on 25 August for the rape of two of his female devotees.