An Israeli military spokeswoman had no immediate information on the incident near the border with Egypt, where soldiers and resistance fighters have frequently clashed during a four-year-old Palestinian uprising.
Witnesses said Nuran Did was lining up with classmates on Monday to enter their school in the morning when she was shot from the army's Termit post, 900m away.
"She suddenly screamed and fell to the ground, bleeding. The girls started to run everywhere," one witness said.
The Palestinian resistance group Hamas said it fired five mortar shells at a Jewish settlement in the Gaza Strip in retaliation for the girl's death.
Witnesses said the shelling damaged a home in Neve Dekalim. There was no immediate word on casualties.
Shot in the head
Doctors at Rafah hospital, where the 10-year-old was pronounced dead, said she was shot in the head.
Violence has dropped sharply in the Gaza Strip over the past two weeks after efforts by new Palestinian President Mahmud Abbas to coax fighters into a ceasefire. The latest death has strained a ceasefire brokered by Abbas.
Palestinian security forces have deployed across the occupied territory in a sign of Israeli-Palestinian cooperation, but they have not been stationed near the flashpoint Termit post, local residents said.
In a separate development, Israeli occupation forces have moved Shaikh Jamal Abu al-Haija, a Hamas leader in the West Bank, to solitary confinement in the Bair al-Saba prison, Aljazeera's correspondent in Palestine reported.
Shaikh Abu al-Haija's health is deteriorating. His right hand was amputated after he sustained injuries due to Israeli fire in the Jenin refugee camp.
Shaikh Abu al-Haija's arrest has been extended many times on charges of links to Hamas' military wing, the Izz al-Din al-Qassam Brigades.