The university announced that it would shut down all residences with immediate effect. It said students must vacate residences within the next 72 hours.
It said the start of term 2 would be announced later.
A medical student at the University of Witwatersrand has also tested positive for the coronavirus, the institution said on Sunday.
The university encouraged 350 of its medical students to undergo self quarantine.
University spokesperson Shirona Patel said all contact classes, tests and face-to-face interactions had been cancelled for Monday. Students in residences were asked to remain in rooms. Employees would be required to report to work, but to take precautions.
All travel was suspended and graduations postponed.
Teaching and learning activities, including tests, have also been postponed at various institutions across the country, including the universities of Johannesburg and KwaZulu-Natal.
In contrast, the Nelson Mandela University said its “classes, tests, laboratory sessions, practicals and experiential learning activities will continue as normal”.