Arindam Battacharya said it was a personal conversation between him and a friend which was made public on social media.
The vice chancellor of the 164-year-old varsity, Sonali Chakraborty Bandyopadhyay, said the decision was taken in the interest of students.
The VC said the vaccination drive will be funded by the state-run university and will be carried out in two campuses.
As many as 15 Indian universities have made it to the ARWU 2020, also known as Shanghai Ranking, released recently.
Holidays and vacations will have to be factored in before chalking out the academic calendar, he said.