NHS Tayside said there were now 68 cases at Parker House – a private accommodation which is home to first year students at Dundee and Abertay Universities – and 16 cases at the Abertay University's Meadowside Halls.
The health board said testing kits have been made available to all residents.
All 500 students Parker House have been asked to self-isolate for 14 days.
Dr Daniel Chandler, chairman of the NHS Tayside Incident Management Team, said there have been no reports of positive cases experiencing serious illness or complications.
He added: “We are expecting an increase in the number of students moving to the local area this weekend ahead of starting their courses, and our university and college colleagues have put in place a number of measures to help protect the student population and to limit the spread of the virus.”