UNESCO's executive board approved the Arab-sponsored resolution at a meeting at the organisation's Paris headquarters.
The text repeatedly refers to only the Islamic name for a hilltop complex in Jerusalem that is also the holiest site in Judaism.
The Palestinian deputy ambassador to UNESCO is Mounir Anastas.
"It is very important to say that this resolution just reminds Israel that they are the occupying power in East Jerusalem, and it asks them to stop all their violations, especially in the fields of competence of UNESCO, such as the excavations and such as the censorship on the scholastic programs and so on."
Last week, Israel suspended its ties with the cultural body over the draft.
It used only the Islamic name for the site that includes the Western Wall, a remnant of the Biblical temple and the holiest site where Jews can pray.
Jews refer to the hilltop compound in Jerusalem's Old City as the Temple Mount.
Muslims refer to it as al-Haram al-Sharif, Arabic for "the Noble Sanctuary," and it includes the Al-Aqsa mosque - Islam's third holiest site - and the golden Dome of the Rock.
Israel's ambassador to UNESCO, Carmel Shama-Hacohen, has denounced the move.
"We will not negotiate, and we won't take a part in this ugly game. There is no place for those games here in UNESCO."
He says UNESCO was established to preserve the history, not to rewrite it.
"And the Palestinians and Arab countries want to rewrite the history of Jerusalem. And we don't need any approval, not from the Palestinians, with all due respect, and even not from the executive board. The history link between the Jewish people and Jerusalem is so strong that nobody on earth can break it. "
The Palestinian representative to UNESCO, Elias Sanbar, says there had been time to negotiate the text.
"Our door has been opened since four weeks - four weeks to negotiate the text. We didn't have one single proposal. Neither from Israel, neither from the European countries who either abstained or voted against it. Not one single word. Four weeks."
Israel and the United States suspended funding to UNESCO in 2011 after the Palestinians were admitted as members.
As a result, both countries lost their voting rights.
A former Israeli Labour Cabinet member, Yossi Beilin, has told Al Jazeera the move does not help relations between Israel and the Palestinians.
"This is, in my view, one bridge too far for the Palestinians. Once you are losing people like myself - and you need the peace camp in Israel - then I think that you are committing a very big mistake, because, eventually, it is against your interest, because we are all dealing now with this foolish sentence which differentiates between Christians and Muslims and Jews, rather than with the real situation on the ground."
