Aljazeera's correspondent in Gaza reported that Ghadir Mukhaimar, 10, died of her injuries at a Gaza hospital on Wednesday after the previous day's attack.
He said Ghadir was sitting in her clasroom in Khaldiya school in western Khan Yunus when an Israeli sniper opened fire from a nearby settlement, injuring her seriously in the chest.
"We have received the news of Ghadir's death sadly," Ghadir's uncle, Muhammad, told Aljazeera.
"It is very painful to lose this flower... Everyday, our people give away martyrs."
He added: "We don't expect any justice from this spiteful occupier. The Zionist occupation forces have not even allowed us to bury our martyr now.
"What kind of justice is this when we cannot bury this innocent little girl? We are waiting for their permission. We may be kept waiting until this afternoon or even tomorrow to bury her."
A spokesman for the UN said on Tuesday that it had repeatedly called on the Israeli army to control the fire of their soldiers in the vicinity of schools.
"We don't expect any justice from this spiteful occupier. The Zionist occupation forces have not even allowed us to bury our martyr now"
Ghadir Mukhaimar's uncle
"It is the fourth incident in under two years. Just last month, a 10-year-old girl died after being shot at her desk," Paul McCann said.
An Israeli military source said soldiers had opened fire on Palestinian gunmen who had apparently taken up position near the school after shooting anti-tank missiles at a nearby Jewish settlement and an army position.
Israel says Palestinian resistance fighters use populated areas for cover thus endangering the lives of civilians.
The incident threatened to escalate tensions between Israel and the United Nations Relief and Works Agency, which runs the school.
UNRWA, the main UN agency for Palestinian refugees, has accused Israeli occupation troops of firing indiscriminately in crowded areas.
UNRWA says Israel has attacked
its schools at least four times
Israeli-UN relations have been strained for years, with Israel repeatedly accusing the world body of bias.
A UN team is in Israel to investigate Israeli allegations that a UN Palestinian driver loaded what appeared to be a rocket into a UN ambulance during a recent Israeli invasion of northern Gaza.
More than 110 Palestinians, mostly civilians and many of them children, have been killed so far in what the Israeli army calls Days of Penitence, the Gaza raid that was launched on 28 September.