The pupils were leaving St Helen's Primary in Bishopbriggs on Thursday when a gunman opened fire on a man collecting his child.
Police fear a number of pupils witnessed the attack which left a 33-year-old man injured.
East Dunbartonshire Council was offering support to young people, it said.
The school was cordoned off after the incident which saw armed police deployed to Dornoch Place at about 3:10pm, as pupils were leaving for the day.
A man approached the victim and fired a hand gun. He then made off on foot in the direction of Ronaldsay Drive.
The man is described as being in his mid 40s, around 5 foot 10 to 6 foot in height with a heavy build. He was wearing a high-visibility reflective yellow colour jacket with the hood pulled up and in possession of a silver-coloured hand gun.
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."