The incident happened in Brunton Street, Cathcart, at around 12:20am.
Police believe the man was involved in an altercation with two Asian men who left the scene in a black Audi A5.
Detectives are now appealing for witnesses and information in relation to the serious assault.
The first man is described as in his late 20s, short and wearing dark clothing. The second man is described as being taller and older.
Detective Inspector Lynsey Watters, of Cathcart CID, said: “This type of violence will not be tolerated and extensive enquiries are underway to get to the bottom of what happened and trace the men responsible.
“I am appealing to anyone who was in the area in the early hours of this morning and may have noticed a disturbance, or a black Audi A5 driving at speed, to please come forward.
“I would also urge motorists with dashcams who were in the Cathcart area at the time to check their footage in case they may have captured something which could be of significance to our investigation."
Police confirmed that the injured man was taken to the Queen Elizabeth University Hospital for treatment to stab wounds and that medical staff described his condition as stable.
Anyone with information should contact Cathcart CID through 101, quoting incident number 0043 of Tuesday, 1 September, 2020. Alternatively you can call Crimestoppers on 0800 555 111 where details can be given anonymously.