Officers were called to St George's RC Primary School on Muirdyke Road but they said there was no risk to children.
A police helicopter has also been sent out as a major probe is launched into the incident.
"Around 9.05am on Monday, police received a report of a firearm being discharged on Muirdyke Road in Penilee. Extensive inquiries are under way to establish the full circumstances of the incident. Additional patrols have been put in place," said a Police Scotland spokesperson.
Glasgow City Council also confirmed that "all pupils and staff are safe" after the incident, which occurred outside the school grounds.
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