The University of Glasgow confirmed on social media it is dealing with a coronavirus outbreak at two student residences - Cairncross House and Murano student village.
Those who are self-isolating are being provided with food and other supplies, the university said.
An incident management team meeting is taking place on Wednesday afternoon.
A spokesman for the University of Glasgow said: "We are aware of two significant clusters of positive cases of Covid-19 in our Murano Street and Cairncross residences, which we believe were largely due to social activity around September 12-14, the start of freshers' week.
"We are working closely with NHS Greater Glasgow and Clyde's public health team to manage these.
"The total number of reported cases since the start of term is 124 but the actual number is likely to be higher.
"Over 600 students are isolating across all residences.
"We are not aware of any students who have had to receive hospital treatment."
National clinical director Jason Leitch said there has been a number of Covid-19 cases confirmed at universities across Scotland.
Some students at Dundee and Aberdeen universities have already been asked to self-isolate.
During the daily coronavirus briefing, he said: "We need you not to have house parties, I could not be more clear."
Nicola Sturgeon said the "significant outbreak at the University of Glasgow" had impacted on the daily Covid-19 infection figure for the NHS Greater Glasgow area.
A total of 224 cases were recorded across the health board area in the past day, she said.
Prof Leitch said he had spoken to student leaders about the latest restrictions on Tuesday through the National Union of Students.
He said: "We discussed what more they could do and what more messaging they could help us with.
"There are now a number of outbreaks in our higher and further education institutions around the country, with significant numbers of positive cases.
"We need every student across Scotland to help us stop the spread of the virus."
Addressing students directly, he reiterated the Government's public health advice on coronavirus and urged people to download the Protect Scotland app.
It is "vital" those asked to self-isolate do so for 14 days, he said, remaining in accommodation and not going out for any reason.
Those self-isolating must try to avoid close contact with others in shared accommodation.
Reporting by PA
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