"54-year-old Bhavna Chauhan was arrested late last night from Unjha town in Mehsana district and has been brought to Vadodara," district police said in a statement.
She had joined as a rector one month ago, it said.
In the FIR, the complainant said she was raped by Patel at his residence, located near the girls' hostel, after Bhavna took her there on Friday night.
The victim had also accused Bhavna of abetting the crime.
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"Patel's residence has been found locked. His whereabouts are yet to be known, but we are confident that he would be nabbed soon," a police officer said.
Meanwhile, BJP MLA Madhu Srivastava from Waghodia, had given a bandh call in Waghodia town demanding Patel's arrest. Most of the shops and other commercial establishments remained closed today, although schools were open.
The university is located at Limda village of this Waghodia tehsil in the district.
Srivastava said, "I have urged Chief Minister Anandiben Patel to take strict action against Jayesh Patel."
"Patel resigned from the post of president as he was accused of being involved in a rape case. We have accepted his resignation. We have complete faith in the judiciary and hope police would investigate the case without bias and bring out truth," it said.