Police said "small flying objects, possibly belonging to drones" were found at both sites.
The UAE vowed reprisals after a drone attack on Monday claimed by Yemen's Houthi rebels triggered a fuel tank blast that killed three people in Abu Dhabi.
The United Arab Emirates is part of a Saudi-led military coalition that supports Yemen's government against the Iran-backed Houthi rebels, who have repeatedly targeted Saudi Arabia with cross border strikes.
But this is the first deadly assault on its own soil acknowledged by the UAE and claimed by the rebels, who said they had fired ballistic missiles and deployed armed drones.
Two Indians and a Pakistani working for oil giant ADNOC died as three petrol tanks exploded near a storage facility, while a fire also ignited in a construction area at Abu Dhabi airport in the heart of the UAE, a renowned safe haven in the volatile Middle East.
Police said "small flying objects, possibly belonging to drones" were found at both sites. Drone attacks have been a hallmark of the rebels' assaults on neighbouring Saudi Arabia.
"We condemn the Huthi terrorist militia's targeting of civilian areas and facilities on UAE soil today... this sinful targeting will not go unpunished," UAE Foreign Minister Abdullah bin Zayed Al-Nahyan said in a statement, as his ministry described the attack as a "heinous criminal escalation".
Houthi military spokesman Yahya Saree said that they had "carried out... a successful military operation" against "important and sensitive Emirati sites and installations" using both ballistic missiles and drones.
The incident follows a surge in fighting in Yemen including advances by UAE-trained troops. The rebels also seized a UAE-flagged ship and its international crew earlier this month.
Saudi Arabia, Bahrain, Qatar and the Organisation of Islamic Cooperation all condemned the "terrorist" attack. Eight Houthi drones targeting Saudi Arabia were also intercepted, the coalition said.
The rebels have previously threatened to target Abu Dhabi and Dubai, the gleaming crown jewels of the UAE which last year opened its first nuclear power plant.
- 'Clear warning' -
Abdul Ilah Hajar, adviser to the president of the Houthis' Supreme Political Council in Sanaa, said it was a warning shot from the rebels.
"We sent them a clear warning message by hitting places that are not of great strategic importance," he told AFP.
"But it is a warning if the UAE continues its hostility to Yemen, it will not be able in the future to withstand the coming strikes."
Saudi Arabia's foreign ministry condemned "in the strongest terms the cowardly terrorist attack" while Bahrain and Qatar also slammed the strikes.
The incident comes two weeks after the rebels hijacked the UAE-flagged Rwabee, and released footage purporting to show military equipment on board.
The UAE said the Rwabee, whose 11 crew are now hostages, was a "civilian cargo vessel" and called the hijacking a "dangerous escalation" in the busy Red Sea shipping route.
The rebels later rejected a UN Security Council demand for the ship's immediate release, saying it was "not carrying... toys for children but weapons for extremists".
Yemen's conflict has been a catastrophe for millions of its citizens who have fled their homes, with many on the brink of famine, in what the UN calls the world's worst humanitarian crisis.
The UAE joined the coalition against the Houthis before announcing a change of tack in 2019.
The pro-government Giants Brigade troops, backed by the Saudis and UAE, recently delivered a significant blow to the rebels by recapturing three districts in Shabwa governorate.
The clashes were part of an upswing in violence in the shattered country, where the war is being fought on several fronts.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)