The UN agency for Palestinian refugees (UNRWA) said Raghda al-Assar was struck in the head on Tuesday while sitting at her desk in one of its elementary schools in Khan Yunis.
Another three Palestinians in the area also sustained moderate wounds when troops opened fire, but none was near the school, medics said.
The UN agency said it was the third shooting incident to have resulted in a pupil being wounded in UNRWA-run schools in the last 18 months.
The agency said the shots came in response to the firing of a homemade rocket by Palestinian fighters in Khan Yunis at the nearby Jewish settlement of Neve Dekalim in the Gush Katif bloc.
“Israeli military positions in Gush Katif retaliated with sporadic gunfire targeted at the western part of the Khan Yunis refugee camp,” it said.
Israeli military sources said the incident was under investigation but insisted that “at no time was a school targeted by our forces”.
They said, however, that troops had returned fire in three instances on Tuesday in response to the firing of mortars and light weapons fire by fighters.
Meanwhile, another two Palestinians were moderately wounded by Israeli gunfire in the southern border town of Rafah when troops opened fire in their direction, medical sources said.