The girl, who was later identified as Basma Awal al-Nadri, a Bedouin high school student, had tried to enter the base and been stopped, Finsi said.
Search for explosives
Police used robots to inspect the body of the girl for explosives.
"She was carrying a backpack, raising suspicions that she was planning a suicide mission. But it turned out she was not carrying explosives," he said.
No guards were wounded in the incident.
The shooting occurred several hours after Israeli troops shot and killed two Palestinian fighters near the border fence with the Gaza Strip.
Israeli security forces said they entered several hundred meters into northern Gaza after spotting several fighters advancing towards the border. They also said an explosive device was found in the area.
Palestinian medics said they recovered two bodies and brought them to a hospital.
The Islamic Jihad and the Popular Resistance Front Committees each claimed one of the slain men as members of their respective groups.
Despite a tenuous ceasefire achieved since Israel ended the 22-day war in Gaza, sporadic attacks have sparked fears that larger clashes may develop between Israel and Palestinian fighters.