More than 100 firefighters and emergency personnel were deployed to the university campus and to Table Mountain National Park. Four helicopters were being used to drop water on threatened areas, officials said.
One firefighter was injured and being treated at a hospital, according to the Cape Town fire and rescue department.
Residents have been cautioned to be on alert, Charlotte Powell, spokeswoman for the city's disaster risk management centre, said in a statement.
"At this stage, there's no cause to evacuate, but we ask that residents adhere to the following: close all windows to prevent draft and reduce heat, damp down your garden using a hose or irrigation system," Powell said.
- AP