Several university buildings were evacuated and nearby roads closed after the discovery on Wednesday morning.
Assistant Chief Constable Steve Johnson said: “Police Scotland officers are continuing inquiries after a suspicious package was received at the University of Glasgow today.
“The package was not opened and no-one was injured. The emergency services were alerted and several buildings within the estate were evacuated as a precaution. A controlled explosion of the device was carried out this afternoon by EOD (explosives ordnance disposal).”
A number of police cordons in and around University Avenue will be in place until further notice, he said.
Mr Johnson added: “There is no ongoing risk to the public. Police Scotland is liaising with the Metropolitan Police in relation to their investigation into packages received in London yesterday.
“However, it is too early to say whether there is a link.”