The draft resolution, which also called upon Israel to join the Nuclear Nonproliferation Treaty, was backed by 15 Arab countries, along with Cuba, Indonesia, Iran, Malaysia and Venezuela.
But Canada sponsored a 45-29 "no action" ballot on Friday that prevented member states from voting on the motion.
Among those supporting the effort to block the vote were the United States, Israel, France, Germany, Britain and Finland, which was at the conference on behalf of the European Union.
Nineteen countries, including Russia and India, abstained.
The final session of the UN nuclear watchdog agency's weeklong meeting did pass a milder resolution on Israel which affirmed "the urgent need for all states in the Middle East to accept full-scope International Atomic Energy Agency (IAEA) safeguards on all their nuclear activities".
The milder resolution - which had also been initiated by the nations behind the defeated resolution - was passed by 89 votes to two.
Israel and the United States were the two "no" votes.
Arab nations have regularly threatened to submit such resolutions at the annual conference, but in past years have opted instead to voice their concerns about Israel's nuclear programme through a statement from the conference president, which carries less weight than a resolution.
The last time such a resolution was submitted at the IAEA conference was in 1991.
But Israel's recent offensive against Hezbollah in Lebanon and what is seen as double standards in the differing ways Israel and Iran have been treated over their nuclear activities added new impetus to the call.
Israel neither confirms nor denies its nuclear status but most experts believe it has about 200 nuclear warheads.
Israel said that a regional nuclear arms-free zone was a noble idea in principle but "frivolous" and dangerous as long as some neighbours continued not to recognise it and with Iran openly calling for its destruction.