A sub-inspector sent to Ahmedabad delivered a notice to the godman, who enjoys a wide following in and outside India, asking him to appear before police on or before Aug 30, a senior officer told IANS.
"Asaram Bapu will be interrogated when he makes himself available for questioning," said the official.
Asaram Bapu's supporters have vociferously denied the allegation -- and so has the spiritual leader.
The aged Asaram Bapu has claimed that police in Rajasthan were acting under "pressure" -- an euphemism for the Congress party which governs the state.
The victim filed a complaint at a police station in New Delhi Aug 20, accusing Asaram Bapu of sexually assaulting her at his ashram in Jodhpur city in Rajasthan.
A first information report (FIR) was registered against him in Jodhpur the next day after receiving a copy of the complaint from Delhi Police.
The officer said police had also issued notices to the warden of a hostel in Asaram's Chhindwara gurukul in Madhya Pradesh where the girl stayed while pursuing her studies.
The godman's personal caretaker has also been asked to appear before the Jodhpur police by Aug 30, the officer added.
Asaram Bapu has been booked under the Protection of Children from Sexual Offences Act and other sections of the Indian Penal Code.
A police team inspected the spiritual guru's ashram near Jodhpur last week and recorded statements of several people to verify whether the girl and her parents were at the ashram on Aug 15 when the girl says she was sexually assaulted.
"During preliminary investigation, it has come up that the girl and her parents and also Asaram Bapu were present at the ashram Aug 15. The owner of the land, which is used for the ashram, told police that the girl and her parents had come to the ashram," said the official.
Asaram Bapu's supporters had earlier claimed that the godman was not in Jodhpur on Aug 15.
Asaram Bapu has reportedly taken refuge in Bharatiya Janata Party (BJP)-ruled Madhya Pradesh, with a party leader, Prabhat Jha, come out in his defence.
The case filed against Asaram Bapu "is a well planned conspiracy" of the Congress, Jha told the media.
The issue figured in parliament Monday.
As the Lok Sabha discussed the gang rape of a photojournalist in Mumbai, Lok Janshakti Party chief Ram Vilas Paswan demanded action against Asaram Bapu.
Janata Dal-United leader Sharad Yadav was vocal: "There is one sadhu who is taking the country for a ride. What have you done in that case? A young girl has slapped rape charges against him.
"The government should say something and do something on this. Why don't you speak on this," Yadav said, looking at Home Minister Sushilkumar Shinde.
"Punishing this sadhu will send a strong message across the country," Yadav added.
Communist Party of India's Gurudas Dasgupta also demanded stringent action against Asaram Bapu.
Shinde, however, said he had no information regarding the case, saying it was a state subject.