The girl fell ill at Moat Community College in Highfields, Leicester, at around 11.30am last Tuesday. Emergency services attended the school but she died a short time later.
Trained counsellors are offering support to students and staff at the school, the Leicester Mercury reports.
Principal Brian Killeen said: "Everyone at Moat Community College is devastated by this tragic event.
"We are in touch with the pupil’s family and our thoughts are with them all at this dreadful time.
“We will be continuing to offer support to our students and staff over the coming days and weeks.
“The city council is providing trained counsellors who have been on site since Thursday morning to offer help to those who need it.
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“What caused this tragic event has not yet been established, so it would not be appropriate to comment further at this stage.”
An air ambulance, three paramedics and a crewed ambulance attended the incident.
A spokesman for East Midlands Ambulance Service said: "We received a call at 11.32am on Tuesday, October 12 to Maidstone Road, Leicester.
"The caller reported a medical emergency. We sent three paramedics in ambulance cars, a crewed ambulance and the air ambulance was also in attendance."
A spokesman for Leicestershire Police confirmed the death was not being treated as suspicious.
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A spokesman for the force said: "Shortly before midday on Tuesday, October 12 a call was received from the East Midlands Ambulance Service stating an 11-year-old girl had gone into cardiac arrest at a school in Maidstone Road, Leicester.
"Officers attended but sadly the girl died a short time later.
"Her death is not being treated as suspicious and a file has been prepared for HM Coroner."