Students were ordered from the campus this morning after the alarming discovery was made about 10:50am.
Police Scotland officers have sealed off part of the campus.
Hundreds of students have been affected by the closures.
The University of Glasgow tweeted from their official account: “Under advice from Police Scotland, a number of buildings on the main university campus have been evacuated as a precautionary measure after a suspicious package was found in the university’s mailroom.
“Police are dealing with the matter and we will provide regular updates.”
The Boyd Orr building, the university’s mailroom and the Wolfson Medical and Bower buildings are among those to have been shut.
Others sites closed are the Isabella Elder Building, James McCune Smith Learning Hub and the Joseph Black Building.
Classes in these buildings have been cancelled for the rest of the day.
University Gardens and part of University Avenue have also been cordoned off by police.
A Police Scotland statement said there was nothing to link the Glasgow University discovery with a separate case in which a suspicious package was found at the RBS building in Gogarburn this morning
“Around 10:50am, on Wednesday 6 March, police received two reports of suspicious packages found at the University of Glasgow and the Royal Bank of Scotland in Edinburgh.
“Emergency services are in attendance and both buildings have been evacuated.
“At this stage there is nothing to link these incidents. The items will be examined and enquiries are ongoing.”
The finds come just 24 hours after explosives were sent to three London transport hubs - Waterloo station and buildings near Heathrow and London City airports.