Israel Radio said, without citing a source, that most of those killed at the United Nations school were children.
"Such a massacre requires more than one hospital to deal with it," said Ayman Hamdan, director of the Beit Hanoun hospital.
The Israeli military had no immediate comment on the incident reported as a truce between the Jewish state and Hamas-led Islamist guerrillas remained elusive, despite intensive attempts at mediation.
Ashraf al-Qidra, spokesman for the Gaza Health Ministry, said that as well as the 15 dead, another 200 people were wounded in the attack. The director of a local hospital said various medical centers around Beit Hanoun in the coastal enclave were receiving the wounded.
Pools of blood lay on the ground and on students' desks in the courtyard of the school near the apparent impact mark of the shell, according to a Reuters photographer at the scene.