Emirati officials said they were investigating the source of the strike and that the UAE had the full right to respond to such "terrorist attacks".
A diplomatic adviser to the UAE president said it represented a dangerous escalation, whether carried out by "the principal perpetrator" or one of its proxies.
The UAE defence ministry said two other drones had been "successfully" dealt with and that the drones had been launched from the "western border".
It did not elaborate.
The drone that got through hit an electrical generator outside the inner perimeter of the Barakah Nuclear Power Plant, the Abu Dhabi Media Office said.
Radiological safety levels were unaffected and there were no injuries, it said.
The International Atomic Energy Agency said emergency diesel generators were providing power to the plant's "unit 3," and called for "maximum military restraint" near any nuclear power plant, adding that it was following the situation closely.
During the war that began with United States and Israeli strikes against Iran on February 28, Iran has repeatedly targeted the UAE and other Gulf states that host US military bases, hitting sites that include civilian and energy infrastructure.
Iran stepped up such attacks on the UAE earlier this month after US President Donald Trump announced a naval mission to try to open the Strait of Hormuz, which the United States suspended after 48 hours.
Trump spoke with Israeli Prime Minister Benjamin Netanyahu on Sunday, Netanyahu's office said.
Trump said in a post on Truth Social: "For Iran, the Clock is Ticking, and they better get moving, FAST, or there won't be anything left of them. TIME IS OF THE ESSENCE!"
Trump is expected to meet top national security advisers on Tuesday to discuss options for military action regarding Iran, Axios reported.
More than five weeks after a tenuous ceasefire in the conflict took effect, US and Iranian demands remain far apart despite diplomatic efforts to end the war and reopen the strait, the world's most important shipping route for oil and gas.
The US has called for Iran to dismantle its nuclear program and lift its hold on the strait.
Iran has demanded compensation for war damage, an end to a US blockade of Iranian ports and a halt to fighting on all fronts, including in Lebanon, where Israel is battling Iran-aligned Hezbollah.
Trump, who held talks with Chinese President Xi Jinping this week without securing an indication from China that it would help resolve the conflict, has threatened to resume attacks if Iran does not agree to a deal.
A senior spokesman for the Iranian armed forces, Abolfazl Shekarchi, said on Sunday that if Trump's threats were carried out, the US would "face new, aggressive, and surprise scenarios, and sink into a self-made quagmire".
Iranian foreign ministry spokesman Esmaeil Baqaei said the US and Israel had tried to shift the blame for destabilising energy markets following their "unprovoked military aggression against Iran".
with AP
