Officers were called out to Drive Road, Govan, at 2am after they received reports of a disturbance.
Emergency services rushed to the scene, however, police confirmed that a 26-year-old man died.
The block of flats, near to Elder Park, were sealed off following the attack. The entire Drive Road was cordoned off between Skipness Drive and Langlands Road.
Detectives were carrying out inquiries, while a police officer stood guard at the tenement.
Forensic teams, wearing protective white clothing, were also at the scene investigating.
It is understood police are following a positive line of inquiry.
A post mortem will be carried out on the body to establish the cause of death.
As part of inquiries, officers were interviewing anyone who left the street. Locals in the street stopped to look at the cordon.
Residents said they realised it was a major incident.
One man from the area, who did not want to be named, said: "They don't shut down a whole street for nothing."
A local shopkeeper said: "Customers have been saying the police have been there almost all night. This is Govan, though, so you do expect this."
A Scottish Ambulance spokeswoman said they attended the incident.
A Police Scotland spokeswoman said: "At around 2am on Friday officers were called to a report of a disturbance at a flat in Drive Road, Govan. As a result a 26-year-old man has died.
"A post mortem examination will be carried out in due course.
"Police are treating the death as murder."