The girl, Ruqayya Abu Eid, ran at the guard at the entrance to the Anatot settlement, prompting him to open fire, police spokeswoman Luba Samri said.
It was the latest in a near-daily series of attacks since October, mainly stabbings, on Israelis by Palestinians.
More than 180 people have been killed - 155 of them Palestinians.
Over the same period, 27 Israelis have been killed in attacks by Palestinians - stabbed, shot or hit by cars.
Israel says most of the Palestinians were killed as they carried out attacks - either shot by their victims or security forces.
Others have been killed in clashes with Israeli troops.
Police spokeswoman Ms Samri said preliminary investigations suggested the girl had left home with a knife after a dispute with her family and had "intended to die".
But her mother, Reeda Abu Eid, contradicted this, according to Reuters news agency, saying there had been no trouble at home - a tent in the Palestinian village of Anata.
The teenager's father arrived at the scene shortly after the incident and was arrested, Ms Samri said.
The recent rise in violence is blamed by Palestinians on the continued occupation by Israel of the West Bank and the failure of the Middle East peace process.
Israel accuses Palestinian leaders and Islamist groups of inciting the violence.
Several of the most recent incidents have involved Palestinian teenagers.
Last Sunday, a mother of six was stabbed to death at Otniel settlement in the West Bank. A 16-year-old Palestinian was arrested over the murder.
A day later, a pregnant Israeli was stabbed and wounded at Tekoa settlement.
A 13-year-old Palestinian girl who tried to stab a security guard at an Israeli settlement in the occupied West Bank has been shot dead, police say.