News of the top official going on leave for "personal reasons" comes just a day before the university reopens on Tuesday.
Authorities at Banaras Hindu University, or BHU, and several other universities in Uttar Pradesh had advanced the Dussehra holidays to start from 25 September to prevent the protests from spreading.
There were also reports that the government was upset at how the university had dealt with safety concerns raised by its women students.
An inquiry by the Varanasi administration had indicted top university officials of dealing with the student protests insensitively which led to a controversial police baton charge on women protesting sexual harassment on campus.
The police action had provoked waves of outrage from across political parties, students and activists.
The Vice Chancellor has been criticised for not acting on the complaint by the women students and going for victim-shaming instead.
"This was not a case of molestation, this was a simple case of eve teasing that was deliberately staged a day before the Prime Minister's visit," he had told NDTV earlier.
OP Singh, the university's chief proctor had earlier quit on moral grounds and was replaced by Royana Singh, the first woman to be appointed to the top post in the university set up in 1916.
Mr Tripathi had earlier brushed aside reports that the centre wanted him to go on long leave.
"But if am I asked to go on leave, I will resign," he said last week. His term as vice chancellor comes to an end on November 30 and the government has started the process to identify his replacement.
It was during the protests that a woman student was beaten up by cops called in by the university when students demanded to meet the Vice Chancellor. A mobile video shows the woman on the ground as she is beaten with sticks by policemen.
The clip went viral and triggered outrage; Prime Minister Narendra Modi and BJP chief Amit Shah both spoke to Uttar Pradesh Chief Minister Yogi Adityanath who later blamed criminals, not students for vitiating the atmosphere in the campus.
(With inputs from PTI and IANS)