Shortly before the alleged arson incident, protesters hurled stones and bottles at vehicles driving past the campus.
At the university's Westville campus, protesters set fire to a section of the gymnasium and a mobile office.
The protests come after an office building of the HIV/Aids support unit at the Howard College campus in Durban was torched on Monday.
At the Edgewood campus, which houses the university of school education, a car was set on fire.
Students are protesting about funding issues - particularly the 15% of their historic debt that they are required to pay before they are cleared for registration.
The Student Representative Council (SRC) told TimesLIVE on Monday that it had reached an impasse in negotiations with the university managers.