Eid Abu Monshar of the Red Crescent medical service said the teenager from the village of Beit Safa was shot in the head during a clash with settlers near the city of Hebron. He said the youth was comatose in a Hebron hospital. Officials at Al-Ahali hospital in Hebron gave his age as 15.
A second youth was shot in the hand in the same incident, Abu Monshar said.
Israeli police spokesman Micky Rosenfeld confirmed that police believe an Israeli opened fire, hitting the teenager. He said police have detained two Israelis in connection with the shooting.
On Thursday, an 18-year-old Palestinian was shot and killed in a different part of the West Bank, near the Palestinian city of Nablus.
Rosenfeld said police have obtained a military surveillance video showing that a settler opened fire after being attacked by a group of Palestinians in the northern West Bank, killing the teenager.
Some 300,000 Israeli settlers live in the West Bank in heavily guarded settlements scattered among a Palestinian population of around 2.5 million. The Palestinians and the international community deem the settlements to be a violation of international law.
Israeli and international human rights groups have called on the Israeli government to do more to protect Palestinian residents from harassment by settlers, many of whom carry weapons.
Also Friday, thousands of Hamas supporters protested in different locations across the Hamas-ruled Gaza Strip against Palestinian President Mahmoud Abbas and his government in the West Bank, the Western-backed Palestinian Authority.
The protests were sparked by documents from a decade of Mideast peace talks, leaked this week by the Arabic TV station Al-Jazeera. The station alleged the documents show that Abbas was ready to make far-reaching concessions to Israel, including on the fate of several million Palestinian refugees and their descendants.
While Palestinian negotiators told their Israeli counterparts that refugees must be able to choose if they want to return to what is now Israel, Abbas acknowledged in a meeting with Palestinian officials that it would be "illogical" to expect 5 million or even 1 million to exercise the "right of return."
Hamas rejects compromise with Israel, and the leaks have deepened the enmity between the two rival Palestinian factions.
The Hamas protesters Friday called Abbas a "traitor," held posters with his face crossed out and burned him in effigy.
In the West Bank city of Ramallah, seat of the Palestinian Authority, several hundred people rallied in support of Abbas.