The victim hailed from West Bengal and was living at his ashram in Barsana district for several months.
The victim alleged that the accused raped her repeatedly and threw her out of the ashram, when she got pregnant.
The victim then returned home and lodged a complaint with the police there.
A team of West Bengal police, accompanied by the local cops, reached the ashram on Thursday night and arrested the self-styled godman.
"We are taking the "baba" to Bengal, as that's where the complaint was lodge," Superintendent of Police, Mathura, Aditya Kumar Shukla told ANI.
The accused, however, denied the allegations and claimed that the victim wanted to oust him from the ashram and hence had implicated him in a false case.
"I didn't do anything, I don't even know the girl. One day a couple left their daughter with me asking me to take care of her," the accused told ANI.
He also claimed that the family members of the woman had visited his ashram last year and left the victim there, asking him to take care of her.
This comes a day after one woman lodged a complaint alleging sexual exploitation by Kaushlendra Prapanacharya Phalahari Maharaj in Chhattisgarh, on Thursday.
The complaint against 70-year-old Phalahari Maharaj, from Rajasthan, was lodged by a 21-year-old woman hailing from Chhattisgarh's Bilaspur.
Presently, Baba Phalahari is admitted in the hospital.
"The concerned doctor is busy in operation. So, we had no conversation with them. We are waiting for his advice. As soon as we are allowed to talk to the Baba in regards to the matter, we will take the legal proceedings further," Alwar SP Rahul Prakash told ANI. (ANI)