Eleven Security Council members voted in favour while Britain, Germany and Bulgaria abstained after hours of consultations on Tuesday.
The US ambassador to the UN, John Negroponte, described the resolution as "flawed" because it did not condemn "acts of terrorism".
Syria, the main sponsor of the resolution, had earlier changed some of the resolution's language to avoid a US veto, adding an expression of "grave concern" at the recent rise in violence.
It also added criticism of both Palestinian bombings and Israel's targeted assassinations of Palestinian fighters for causing "enormous suffering and many innocent victims".
But Negroponte said the resolution should have explicitly condemned groups such as Hamas and al-Aqsa Martyrs Brigades.
The vote came on a day of bitter exchanges between the Israeli and Palestinian envoys during a debate on the issue. The Israeli ambassador described Arafat as the inventor of global terrorism, comments which the Palestinian envoy dismissed as "trash".
The resolution was put forward after Israel’s Vice Premier Ehud Olmert on Sunday said assassinating Arafat was an option as the Jewish state considered to “remove” him, in comments roundly condemned across the world.
“Killing (him) is definitely one of the options,” Olmert, a member of Israeli Prime Minister Ariel Sharon’s Likud party, told Israeli radio.
Israel’s security cabinet had announced days before it would “remove” Arafat, triggering an outcry from Palestinians and the international community.
Israel has not said when it would move against him. But US reluctance to act against Israel is likely to embolden the Jewish state to take action.