The army said the young Palestinian killed the girl in her bed after breaking into her home in the Kiryat Arba settlement outside the flashpoint city of Hebron.
Security personnel rushed to the house and fired on the attacker, who wounded a guard before being shot dead, the army said.
The girl was taken to hospital in Jerusalem in critical condition and died of her wounds.
The Palestinian health ministry identified the attacker as Mohammed Nasser Tarayra, 19, from the village of Bani Naim, just outside the city, in the south of the Israeli-occupied West Bank.
The victim's family said Hallel Yaffa Ariel, was attacked in her sleep, and the military released a photograph of her blood-spattered bedroom.
As mourners visited the family home, the girl's father told AFP she had been sleeping late after a dance performance the night before and that he had been on his way to the house to wake her for work when he heard of the attack.
She worked in his winery during the summer vacation which just started.
"At the first moment I thought everything was well, but I knew deep in my heart she was not alive," said Amichai Ariel, 59. "I shouted at her."
Israeli Prime Minister Benjamin Netanyahu held talks with Defence Minister Avigdor Lieberman after the attack, and the home village of the assailant was sealed off.
Israeli work permits for members of Tarayra's extended family were also to be revoked and authorities began procedures aimed at demolishing his home, a measure often taken against attackers.
"I expect the Palestinian leadership to clearly and unequivocally condemn this vicious murder and take immediate action to stop the incitement," the premier said in a statement.
"The entire world needs to condemn this murder just as it condemned the terrorist attacks in Orlando (Florida) and Brussels."
Hours later in the town of Netanya, on the Mediterranean coast north of Tel Aviv, a Palestinian from the northern West Bank stabbed a man and woman, both Israelis, before being shot dead by a passing civilian, police said.
Hebron has been a flashpoint in a spate of deadly unrest that has rocked Israel and the Palestinian territories since last October.
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Several hundred Jewish settlers live in a tightly guarded enclave in the heart of the city of more than 200,000 Palestinians, a persistent source of tensions.
Kiryat Arba lies on the outskirts of the city and has a population of more than 7,000.
In New York on Thursday, the UN envoy on Middle East peace said that a report by the diplomatic Quartet, expected to be release on Friday, demands that Israel take urgent steps to halt the expansion of settlements.
Nickolay Mladenov told the Security Council that ongoing Israeli construction in the West Bank was one of three "negative trends" that must be quickly reversed to keep the hope of an Israeli-Palestinian peace deal alive.
Palestinian incitement to violence and the Palestinian Authority's lack of control over the Hamas-ruled Gaza Strip also "severely undermine hopes for peace", Mladenov said.
Violence since October has killed at least 212 Palestinians, 33 Israelis, two Americans, an Eritrean and a Sudanese.
Most of the Palestinians were carrying out knife, gun or car-ramming attacks, according to Israeli authorities.
Others were killed in clashes with security forces or by Israeli air strikes on the Gaza Strip.
Analysts say Palestinian frustration with Israeli occupation and settlement-building in the West Bank, the complete lack of progress in peace efforts and their own fractured leadership have fed the unrest.
Israel says incitement by Palestinian leaders and media is a leading cause of the violence.
On a visit to Israel and the Palestinian territories this week, UN chief Ban Ki-moon condemned the recent wave of attacks as "terrorism".
But he urged Israel to address the "key underlying causes of violence" including "growing Palestinian anger, the paralysis of the peace process, the nearly a half-century of occupation".
Negotiations between the Israelis and Palestinians have been at a standstill since a US-led initiative collapsed in April 2014.
France is planning to hold an international conference before the end of the year in a bid to restart the peace process.
Israel opposes the French initiative, calling instead for bilateral negotiations, while Palestinian leaders have expressed support for it.