The incident was reported from northeast Delhi's Karawal Nagar and the boy, who had pushed the victim, has been apprehended, they said.
The police were informed that a child had fallen unconscious in a school here, Deputy Commissioner of Police (northeast) A K Singla said.
The Class 7 student was taken to a private nursing home and later to a government hospital where he was declared brought dead, the officer said.
"In the fight, the juvenile pushed Prince whose head hit the wall and he fell unconscious," Singla said.
More From This Section
The police have registered a case and begun investigations, he said.
Prince's family has claimed that he was beaten by four of his friends.
However, the police said that no external injury marks were found on his body and that only one student was allegedly involved in the matter.
The exact cause of death would be ascertained in the post-mortem, they said.