Ross Monaghan was seriously injured just yards from St George’s Primary in the Penilee estate in the south-west of city. No one else was hurt.
The 35-year-old is understood to have dropped his child off at the school shortly before 9 a.m.
He was walking along Muirdykes Road when he was approached by a male with his face covered and shot at close range.
The victim was taken to hospital where his condition is described as stable.
Monaghan was cleared of killing gangster Kevin ‘Gerbil’ Carroll, an enforcer for the Daniel crime family, in 2012 in a drive-by shooting.
Billy Paterson, 29, was given 22 years for the murder in 2015 after giving himself up for trial.
One parent told The Scotsman that pupils were lined up in the playground, waiting to enter the school, when a loud “firework-like bang” was heard on Muirdykes Road.
Mary MacLeod, who had returned home after walking her son to school, said: “I heard the bang echo around the houses.
“I immediately left the house when I saw the commotion outside. Parents were standing around in a state of shock.”
The Scotsman understands Monaghan was helped into the school by several parents and staff who had witnessed the incident.
Chief Inspector Simon Jeacocke said: “This is a highly unusual incident and understandably, parents, staff, pupils and people in the local community are all very alarmed by this.
“We do believe it was a targeted attack but nonetheless this took place near to a local primary school at the start of the school day, when the area was busy with parents dropping off their children.
“Although it would appear that there was an intended victim, anyone could have been injured as a result, putting young children and innocent people at risk.
“The pupils are now safe at school and additional police patrols are in the area to provide extra reassurance over the next couple of days.
“Detectives are carrying out enquiries to establish the full circumstances of the incident and are keen to appeal to anyone who may have seen the incident or who had been in the area at the time.”