Three youths managed to gain entry to Holyrood Secondary School as more than 2000 pupils studied in their classrooms.
An investigation has been launched into the incident at the South Side school - Europe's largest secondary - on Wednesday afternoon.
Police, including the school's campus officer, are working with council staff and teachers to establish the full circumstances of the incident.
Officials are also understood to be probing claims they may have been former pupils.
The three youths are understood to have been in the school's reception area, despite security measures to protect children.
One concerned parent said: "I'm walking my son to school from now on, as we don't know who these men are, and what they planned on doing.
"We've not been told anything official either. There was no letter from the school, which hasn't helped."
Council bosses stressed there was no risk to pupils at any time. More than 2000 pupils and 130 teachers are based at the city school.
SNP councillor Mhairi Hunter said the incident was "very concerning" and thought security was "very tight" at Holyrood Secondary.
Councillor Hunter, who represents the Southside Central ward, said: "This is really, really worrying.
"It is very important our schools are safe and secure.
"An investigation is under way and we need to wait for the outcome of that before deciding any measures that need to be taken."
Police confirmed they were called to a "disturbance" at around 3pm on Wednesday.
A spokeswoman said: "There are no reports of any weapons seen. However, we are trying to establish the exact circumstances surrounding the incident and inquiries are ongoing."
Witnesses, or anyone who may have seen the three men in the area, have been asked to come forward.
A Glasgow City Council spokeswoman said: "The school is working with the police to establish the details of the incident.
"No pupils were in the reception area when the youths entered the school and the campus police officer dealt with the situation swiftly."
Anyone with any information is asked to contact Police Scotland on 101.