Armed response teams were sent to Dornoch Place, Bishopbriggs, as pupils filed out of nearby St Helen's Primary School at 3.10pm on Thursday.
Officers confirmed no children were involved in the incident although the school was sealed off as part of the investigation.
Police Scotland said the gunman approached the 33-year-old victim, shot him, then ran off towards Ronaldsay Drive.
The victim is being treated in hospital. No one else was injured, police said.
A major incident room has been set up at Kirkintilloch Police Office and detectives said they are "following a number of lines of inquiry".
The gunman is described as in his mid 40s, around 6ft, of heavy build. He was wearing a yellow high-visibility jacket with the hood pulled up and was carrying a silver hand gun.
Detectives found a burnt out grey Volkswagen Golf in the nearby Wood Lane which they believe is connected.
Chief Inspector Craig Smith said: "Understandably, the local community is very concerned about such a violent incident occurring mid-afternoon in a busy residential area of Bishopbriggs, close to a local school.
"I have officers carrying out high-visibility patrols, engaging with the public to reassure them that we are doing everything we can to establish who is responsible for this incident.
"Detectives are carrying out door-to-door inquiries and are currently gathering CCTV footage for review, and are following a number of lines of inquiry."
Detective Inspector Greig Wilkie said: "I would appeal to anyone in the area of Dornoch Place at this time and could have seen anything suspicious to come forward and help with our inquiry.
"A grey Volkswagen Golf was also recovered burnt out in the area of Wood Lane which is a short distance away and this vehicle is suspected to be involved. I would appeal for anyone who has seen a vehicle of that description near to the incident or where it was recovered to contact the police urgently."
