Swami Poornananda (52) was apprehended under section section 376 (punishment for rape) of the IPC after the victim lodged a complaint against him, they said.
The accused is head of the city-based Swami Gnananda Ashram which houses an orphanage and old-age home.
He was picked up from the Ashram premises along with a woman, police said.
It is suspected that the alleged incident might have taken some three months back as claimed by the girl, police said.
Meanwhile, members of a tribal students association thrashed the accused alleging that he had sexually assaulted other inmates of the shelter as well.