The Israeli army had no immediate comment.
The strike hit the U.N. school in the Jebaliya refugee camp where hundreds of Palestinians had sought shelter from the intense fighting and Israeli tank fire, said Adnan Abu Hasna, a spokesman for the U.N. aid agency UNRWA, which has opened its schools to those displaced by the fighting.
Starting at around 4:30, several tank shells hit the school compound, a few minutes apart, said the school principal, Fayez Abu Dayeh. He said shells hit two classrooms and a bathroom.
In one of the classrooms, the front wall was blown out, leaving debris and bloodied clothing. Another strike tore a large round hole into the ceiling of a second floor class-room.
Ashraf al-Kidra, a Palestinian health official, said at least 15 people were killed and about 90 wounded.
The deadly strike came a day after Israel unleashed its heaviest air and artillery assault in the bloodiest day of the three-week Gaza war, destroying key symbols of Hamas control, shutting down the territory's only power plant and leaving at least 128 Palestinians dead.