Iman Talba was killed in the Amal quarter of the city of Khan Yunis on Saturday when Israeli occupation soldiers from the Ganei Tal Jewish settlement opened fire at her three-storey building nearby.
The Israeli army said it was checking the report.
Talba's cousin, Alaa, told Reuters he saw a bullet fly through the family's kitchen window, ricochet off a wall and hit her. He added there were no clashes in the area at the time.
"Iman had returned from school and was going to the kitchen to ask her mother about lunch," he said.
"While she was getting a plate, a bullet suddenly came through the window and she was shot in her head, with her blood spilling onto the floor."
Israeli military sources said there were three incidents of troops opening fire in the Khan Younis area on Saturday. In two cases, soldiers had "returned accurate fire" at assailants who launched rockets at adjacent settlements.
In another incident, soldiers fired warning shots near an army post to clear the area before checking it for explosives, the sources said.
Elsewhere on Saturday, Aljazeera's correspondent in the West Bank reported that Israeli occupation forces raided the refugee camps of al-Ain and Balata on the west and the east sides of the city of Nablus.
"The occupation forces imposed a curfew on al-Ain refugee camp, demolished some houses and arrested a number of residents, while in Balata refugee camp, confrontations erupted between Palestinian youths and Israeli soldiers", she said.