Medics said teenager Sara Mahmud Zurub was shot in the chest in an outlying neighbourhood of the city of Khan Yunis on Monday and died on the way to the hospital.
"She was outside playing with the other kids and then the shooting started. She was playing soccer," her cousin said.
"After she got shot, the other kids started screaming."
In a separate incident, medics said soldiers shot dead a 50-year-old Palestinian woman in the south of the territory. The army claimed it had fired towards a site where mortars were allegedly fired from.