"The first hurdle has been overcome. We will take our fight forward," the father said after ending his fast after midnight.
He thanked the media saying, "The arrest has been made possible because of their efforts."
The father of the girl had found support from many teachers, doctors, lawyers, traders and others who also sat on a token hunger strike to show their solidarity.
After he ended his fast, the girl's father was taken to his home amid heavy security.
Meanwhile, demonstrations against Asaram were held by Rashtriya Mahila Shakti Dal and others at different places, with protesters burning his effigy.
72-year-old Asaram, who has been booked for allegedly sexually assaulting the teenage girl in a Jodhpur ashram, was arrested after midnight on Saturday in Indore and brought to Jodhpur on Sunday afternoon.