Kyle Rees suffered a serious head injury on Monday at Portchester school in Bournemouth, Dorset.
The police said Kyle was immediately taken to a nearby hospital later transferred to Southampton general hospital, where he died yesterday.
A 16-year-old boy was arrested in connection with the incident, initially for an offence of assault and subsequently on suspicion of manslaughter, the Guardian said.
He has been released on bail while inquiries continue.
Debbie Godfrey-Phaure, the executive head of Portchester school, said, "We are also fully assisting the authorities with their investigations.
Kim Drake, service director for children's social care at Bournemouth borough council, said: "We have set up a counselling service at the school to offer pupils, staff and parents support following this tragic incident at the school and we are currently working with both the school and the police with their investigation."