The Israeli defence ministry said the girl was not carrying a weapon but told officers afterwards that she had wanted to die.
The incident occurred at a checkpoint near the Israeli settlement of Alfei Menashe and the Palestinian town of Qalqilya in the occupied West Bank.
The Palestinian health ministry described the girl's wounds as moderate.
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The Israeli defence ministry said the girl arrived "on foot with a suspicious bag at the vehicle-only lane of the Eliyahu crossing which is not open to foot traffic."
"Guards at the crossing called for her to stop several times and then fired warning shots into the air. When this did not stop her, a single shot was fired at her leg."
A new surge of violence began on Friday after Palestinians wrapped up the Muslim celebration of Eidul Azha and as Israel tightened security ahead of major Jewish holidays in October.
There have been nine attacks or attempted attacks by Palestinians against Israelis since then, according to Israeli authorities.
The upsurge has shattered several weeks of relative calm.
The attacks have included one on Monday in which a Palestinian stabbed two Israeli police officers outside Jerusalem's Old City, leaving one in serious condition and another moderately wounded.
The assailant in that case was shot and seriously wounded.
Violence since last October has killed 230 Palestinians, 34 Israelis, two Americans, one Jordanian, an Eritrean and a Sudanese, according to an AFP count.
Israel says most of the Palestinians killed were carrying out knife, gun or car-ramming attacks. Others were shot dead during protests or killed in Israeli air strikes on Gaza.
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Many analysts say Palestinian frustration with the Israeli occupation and settlement building in the West Bank, the complete lack of progress in peace efforts and their own fractured leadership have helped feed the unrest.
Israel says incitement by Palestinian leaders and media is a main cause of the violence.
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