The official, Kiran Damle, is the deputy chief proctor at the Rajiv Gandhi South Campus of BHU in Mirzapur.
She has been accused of "insulting religious beliefs".
Damle, according to sources, reportedly, removed the flag while students affiliated to the RSS were holding a 'shakha' on Tuesday morning.
Damle has said that she was only following the rules of the institution.
"I asked the shakha members to remove the flag themselves, but they paid no attention. So I picked up the flag and gave it to my peon. When they came after me, I told them that they could not hoist the flag at such a sensitive time. When they insisted, I said I would not allow it inside the stadium," she said.
The students later held protests on the campus, forcing Damle to quit.
A local unit of the RSS the ideological mentor of the ruling BJP filed a complaint and the police registered a criminal case against her on charges of insulting religious beliefs.
After the incident, the RSS members staged a protest at the administrative block claiming that Damle had insulted the flag. The protesters also accused Damle of misbehaving with students.
BHU sources said that they are in talks with senior RSS leaders in Mirzapur to resolve the issue.
Ratnakar Mishra, a BJP MLA who visited the campus during the protests, said, "The RSS has been holding shakhas here for many years now. It was the last wish of (BHU founder) Madan Mohan Malviyaji that any institution started by him should have shakhas. She has insulted his memory."
( With inputs from IANS )