The move seeks to draw worldwide attention to the situation in Hebron, where sites holy to both Jews and Muslims are located.
In a secret ballot, 12 countries voted in favor, three voted against and six abstained.
"In another thousand years, the Cave of the Patriarchs will remain under Jewish sovereignty and UNESCO will cease to exist as a heritage organization, " said. "It's disappointing and disgraceful that time and again UNESCO denies history and distorts reality, knowingly serving those attempting to erase the Jewish state".
The city - which is holy to Jews, Muslims and Christians - is the largest in the West Bank, with more than 200,000 Palestinians and a few hundred Israeli settlers.
Palestinian security sources said the 37-year-old victim, identified as Omar Ahmad Issa, was struck in the town of al-Khader, located 5 kilometers (3.1 miles) west of Bethlehem, at around 4 a.m. local time (0100 GMT) on Friday, while riding his motorcycle near a checkpoint leading to the occupied East Jerusalem al-Quds. Israel's army controls access to the Cave of the Patriarchs.
The vote was held in secret at UNESCO World Heritage Committee's 41st annual summit, now taking place in Krakow, Poland, following a special request, despite decisions usually being made by a show of hands.
Promoting the resolution, the Palestinian Ministry of Foreign Affairs had argued: "Hebron's Old City and holy site is under threat due to [the] irresponsible, illegal and highly damaging actions of Israel, the occupying power".
Netanyahu expressed outrage that UNESCO determined the Tomb of the Patriarchs in Hebron "is a Palestinian site, meaning not Jewish, and that the site is in danger". He said that the decisions of this "irrelevant" organization will not harm the country's right and expressed hope that the United States will stop funding UNESCO. It has taken a tougher line under the Trump administration against what it says is anti-Israel bias among certain United Nations organizations.
In the run-up to the vote, the United States ambassador to the United Nations, Nikki Haley, sent a letter to two senior United Nations officials asking them to withhold the Hebron designation. Abraham, Isaac, Jacob, Sarah, Rebecca, and Leah are all later buried in the same Cave of Machpelah.
It is one of the most important religious sites to Muslims and Jews alike.
The Dutch Prime Minister complained to his Israeli counterpart, Benjamin Netanyahu, about Israel's dismantling of solar panels set up without permission in the West Bank thanks to funding from the Netherlands.