Police were called to an incident at the Shettleston Juniors football ground in Shettleston Road at about 00:35.
A 21st birthday party function had been held at the club earlier.
Four men were taken to hospital. One of them, aged 24, died a short time after admission. The death is being treated as "suspicious".
The other three men discharged themselves from Glasgow Royal Infirmary after being treated for serious injuries.
Det Insp Martin Fergus said: "We are currently viewing CCTV and carrying out door-to-door inquiries in order to establish the circumstances surrounding this incident.
"We know that there had been a 21st birthday party function at the club and I would appeal to anybody who was at the function, or knew of anybody attending the function, to please contact us.
"It is clear that this disturbance took place in the street, therefore if you saw or heard anything, no matter how trivial you may think it is, it is vital that we speak to you."
He added: "I also urge anyone who was passing by the football ground at around 0030 hrs this morning and saw anything suspicious to contact police immediately."
A man has died and three others have been injured after a disturbance outside a football ground in the east end of Glasgow.