Police are appealing for witnesses to the incident which took place on Holmbyre Road at around 3.30am on Sunday, October 18.
The man was walking home when he was stabbed in the side in what the police have described as an unprovoked attack.
Police are trying to trace a man who is described as white and wearing a dark top.
Detective Constable Glenn Clark at Cathcart Police Office said: "I would urge anyone who may have been in the Holmbyre Road area, near to its junction with Blaeloch Drive around this time to contact us if they saw anything which might help in this investigation.
"I would also urge anyone who may have been in a vehicle fitted with a dash-cam to view their device to see if it holds any information which might assist.
"Callers can contact police on the 101 number and should quote the reference 0700 of October 18.”