NHS Lothian said a number of people have tested positive at Edinburgh Napier University’s Bainfield student accommodation.
The health board’s health protection team is tracing contacts and advising them to self-isolate for two weeks but has stressed the university remains open.
NHS Lothian said in a statement: “NHS Lothian’s health protection team are investigating a cluster of cases who have tested positive for Covid-19 in Edinburgh Napier University’s Bainfield student accommodation.
“To respect and maintain patient confidentiality, no further details will be released.
“The health protection team are contacting individuals and any close contacts living in university accommodation.
“Appropriate advice and guidance to self-isolate is being provided. Enhanced cleaning and safety measures are already in place in the university in line with national guidance.
“If someone has been in close contact with a confirmed case, they will be contacted and given advice about what they should do.
“If you have been contacted regarding these cases by NHS Lothian you should isolate for 14 days even if you do not develop any symptoms.
“You do not need to be tested unless you become symptomatic with either a new and continuous cough, a fever, a loss or change in smell or taste.
“The university remains open and operational as normal. All students and staff who have not been asked to self-isolate should continue to attend as normal.”
A spokesman for the university declined to add to the NHS statement.
Last week, ahead of the return of students, a spokesman for Edinburgh Napier University said: “We are all eagerly looking forward to the new academic year, and we have written to students to remind them of their responsibilities during the Covid-19 pandemic and offer appropriate guidance.
“It is important that the health and safety guidelines set by ourselves and the Scottish Government are closely observed, and where behaviours fall below acceptable standards this may be dealt with under Student Conduct Regulations or the terms of their Student Accommodation Tenancy Agreement.
“By working together, we aim to keep our university community and the communities around us safe and free of Covid-19.”