The two boys, aged 13 and 14, were found seriously ill in a house in Gregg House Lane, Shiregreen, and were taken to hospital where they later died.
Four other children, aged 11, 10, three and a baby of seven months, were also taken to hospital, where they remain this afternoon while they receive treatment.
The school, which cannot be named for legal reasons, said: “It is with great sadness that we can confirm that two of our students died in tragic circumstances this morning. As this is a Police matter, we are not able to provide any further detail at the moment.
“Our deepest condolences are with the family and their friends during this difficult time. We will be providing the appropriate support to our students and staff to help them to come to terms with what has happened.”
Emergency services were called to the property at 7.30am and there were multiple police cars and ambulances deployed.
An air ambulance was also scrambled.
The house where the children were found remained cordoned off this afternoon and crime scene investigators in protective white suits are examining the property.
The cause death for both boys has not yet been established.
Post mortem examinations are expected later today.
A 37-year-old man and a 34-year-old woman have been arrested on suspicion of murder in connection and remain in custody.