It is understood that four officers – three men and a woman – were needed to take the weapon from her at the 700-pupil Webster’s High School in Kirriemuir, Angus.
Police rushed to the scene after receiving a call from the school just before 9am on Thursday, October 19.
Angus Council has refused to say whether the girl, who cannot be named for legal reasons, had been suspended from the school.
A source spoke of concerns for the safety of the school’s pupils in the wake of the incident, coming two years after a pupil was killed with a knife at Cults Academy in Aberdeen.
The source said: “Police were called just before 9am to disarm the girl, who was wielding a knife.
“She had made threats to kill a fellow third year pupil. It took three policemen and one policewoman to disarm her. I don’t want Webster’s to be the next Cults Academy.”
A spokesperson for Police Scotland said: “Police Scotland can confirm that they were called to Webster’s High School, Kirriemuir, on October 19 in response to a 13-year old-pupil being in possession of a knife.
“The knife was handed over without incident and the girl is to be reported to the Children’s Reporter for possession of a knife within a school, and for threatening and abusive behaviour.”
Angus Council refused to reveal whether the pupil had been suspended and said: “The matter is the subject of a police report and it would not be appropriate to comment.”
In August last year a pupil from Montrose Academy was excluded from the school following an incident involving a knife.
Parents were sent letters to inform them of a lunch-time confrontation between two “older pupils” in which a knife was shown.
In October 2015 16-year-old Cults Academy pupil Bailey Gwynne was stabbed through the heart by Daniel Stroud — also 16 at the time.
A subsequent report into the Aberdeenshire teen’s death concluded that the incident was “avoidable” and that consideration should be given to changing the law to “improve the resilience of schools”.
Last month Aberdeen City Council implemented a stronger policy to clamp down on weapons in schools.