A school bus was set afire, several shops inside the campus vandalised and CCTV cameras broken, allegedly by students and supporters of the youth leader, Ashutosh Singh.
University officials said the group, which included outsiders, shut the main gates of the university's sprawling campus before going on a rampage.
Police said they had received multiple complaints against Ashutosh Singh over the last few days including one where he was alleged to have barged into Varanasi's IIT-BHU event and created a nuisance.
University officials said they had not allowed the police into the campus and had dealt with the protests with their own manpower, largely private security guards to prevent the situation from escalating.
The last time the university administration had let the police in to handle student protests, it had sparked national outrage after two policemen were caught on camera beating up a woman student with batons.