The attack which left a 35-year-old man injured is now being treated by police as attempted murder.
It is understood the man was gunned down outside St George’s RC Primary School on Muirdykes Road at around 9.05am after dropping his child off at school.
He was approached by another man who was pushing a four-wheel, collapsible-type buggy and then drew a firearm from his back.
The buggy did not have a child within it and no one else was hurt.
But, following treatment for a shoulder injury at Glasgow’s Queen Elizabeth University Hospital the victim has been discharged.
Police have released a description of their suspect as a male, wearing a blue padded jacket, blue jeans, a dark woollen bobble hat and a woollen scarf pulled up around his face.
Detective Chief Inspector John Kennedy appealed for anyone who was in the area at the time to come forward with any information.
He said: “This was a particularly distressing incident for the local community, given it took place close to a primary school.
“Although our investigation is at an early stage, we are carrying out a number of enquiries to establish the exact circumstances of the incident but I do believe that this was a targeted attack focused on one intended victim.
“Whilst forensic and ballistic examinations continue to take place at the scene, detectives are carrying out door to door enquiries in the area and reviewing CCTV.
“This is a highly-populated, residential area and I am appealing to anyone who may have seen the man with the buggy before or after the incident to come forward with any information.
“This was a busy time at the start of the school day and although most children were already in school, parents will still have been around its vicinity.
“You may have seen something unusual or somebody acting suspiciously in the area.
“Any information could help us find the person responsible for this incident and I would urge people to contact Govan Police Office on 101 or alternatively call CRIMESTOPPERS on 0800 555 111, where calls can be received anonymously.”
Chief Inspector Simon Jeacocke said: “People in the community are shocked and alarmed at this morning’s incident and I have high-visibility officers patrolling the area to provide reassurance.
“We are also working closely with our colleagues in Education Services at Glasgow City Council to ensure that pupils, staff and parents are provided with support and information and we have specialist resources such as the mounted branch providing visible, additional support.
“I would urge anyone who is concerned about the incident to approach my officers who will provide assistance.”