About 10 cases of the contagious illness have been confirmed at the university.
The university's student health team is now offering free measles, mumps and rubella (MMR) booster shots to students who have not had two MMR vaccinations since 1990, or are unsure of their vaccination history.
Clinics are being held today and tomorrow.
Pro-vice-chancellor of health sciences Professor Peter Crampton, the convener of the university's pandemic planning group, said the group was ''closely monitoring the evolving situation''.
"The Pandemic Planning Group is determining our ongoing response as the situation develops."
All students and staff had been emailed information regarding mumps, and advice had been posted on social media.
Mumps is spread by coughing and sneezing, or through saliva, and causes swelling of the glands around the face and body.
While it usually takes between 12 and 25 days for symptoms to present, including pain in the jaw, fever, headache and swollen glands, people with mumps are infectious for seven days before swelling occurs until five days after.
SDHB Medical Officer of Health Dr Keith Reid said in a statement the cases seem to follow the trend of an increase in community acquired mumps cases in New Zealand.
"It seems that the original source was overseas but that mumps is now established and circulating in Auckland and some other towns and cities. The Dunedin cases appear to have caught mumps in New Zealand,” he said.
Public Health South staff, the university and Student Health have been wroking closely together during the outbreak, he said.
"We are encouraging students who have not had 2 MMR to get immunised as this offers the best protection against the infection. Immunisation with MMR is free,” Dr Reid said.