Detectives investigating the attack, which happened on Thursday morning in Shawhill Road, Shawlands, say the male victim was targeted.
Police said a 34-year-old man was treated at Queen Elizabeth University Hospital in the city for gunshot injuries.
Extensive enquiries are ongoing in the area to establish the exact circumstances surrounding the shooting.
Detective Inspector Colin Hailstones, of Cathcart CID, said: “At around 9.35am, on Thursday March 9, officers were informed that a man had presented at the Queen Elizabeth University Hospital with injuries which are consistent with a firearm having been used.
“The 34-year-old man has now left hospital having received treatment for a serious injury.”
Police say there will be an increased uniform presence in the area following the shooting.
They received no reports of a firearm being used and are trying to reassure concerned members of the public.
Mr Hailstones added: “We know that local residents will be concerned by this incident.
“From what we understand, this was a targeted and isolated attack which is being treated by police as attempted murder.
“We have had no reports of firearms having been discharged, however enquiries are ongoing to determine the circumstances surrounding the incident.
“As part of those enquiries, officers are currently searching the area around Shawhill Road.
“There is an increased uniformed presence in the area alongside and I would ask local residents to approach those officers with any information or concerns that they have.
“I am particularly keen to appeal to anyone who may have seen or heard a disturbance in the area around that time on Shawhill Road.
“Alternatively, call Crimestoppers on 0800 555 111, where information can be given in confidence.”