The 34-year-old was getting into his vehicle in Shawhill Road, in Shawlands, at about 08:30 when he noticed a man near his driveway.
When he went to investigate the man shot him once in the leg.
Police said the victim chased his assailant but he got into a car and was driven away. The attack is being treated as attempted murder.
The injured man received hospital treatment but was later released.
The gunman is described as 5ft 7ins tall, wearing dark clothing and a dark beanie hat.
Det Insp Colin Hailstones of Cathcart CID, said: "We now understand that the incident occurred around 0830 hours this morning in a highly-residential street in the Shawlands area.
"The 34 year-old man was shot at once and he received injuries to his leg and has been treated in hospital. He has since been released.
"I know that local residents will be concerned by this incident. We understand that this was a targeted and isolated attack. It is being treated as attempted murder.
"Detectives are currently searching the area around Shawhill Road, Pollokshaws Road and St Ronan's Drive. Specialist officers will be conducting work in the area alongside detectives and we are conducting door to door enquiries and assessing opportunities to capture CCTV.
"We will not allow such a brazen act of violence to go unaccounted for."
The gunman fled into Hector Road and towards Pollokshaws Road and continued into St Ronan's Drive where he got into the passenger side of a dark-coloured car.
A man who was shot in the leg by a gunman in Glasgow chased after his attacker, police have revealed