Air defences took down the projectile at 12.20am as it flew towards the Emirates.
There were no casualties and the fragments of the ballistic missile fell in different unpopulated areas, Wam reported.
"I’ve directed Secretary [of Defence Lloyd] Austin to do everything he can to communicate the support of the United States for the UAE, Saudi Arabia and throughout the Gulf region," said US President Joe Biden from the White House while hosting Qatari Emir Sheikh Tamim bin Hamad Al Thani.
"America will have the backs of our friends in the region."
A subsequent strike on a target in Al Jawf province, outside Houthi-controlled Sanaa, destroyed a missile platform and the launch site, the ministry said in a tweet.
The ministry reiterated its "full readiness to deal with any threats", adding it would "take all necessary measures to protect the UAE from any attacks". Officials called on the public to only follow news from official sources.
Dr Anwar Gargash, diplomatic adviser to President Sheikh Khalifa, said on Twitter that the country will not be distracted from its part in "building a stable and prosperous region for all".
"We are determined to achieve our goals and strategic vision to build a stable and prosperous region for everyone. Provoking us will do no good.
"We do not see the threats of terrorist organisations and their fantasies based on illusions as more than something that will pass and be handled in a way that guarantees our security and national sovereignty. Those who test the UAE are mistaken to do so."
The General Civil Aviation Authority, which regulates air travel, on Monday said that "air traffic movement is normal and all flights are operating as usual", in a Wam statement.
"There is no impact on flights and airports resulting from the interception of the ballistic missile launched by the Houthi terrorist militia on the country," it added.
The US denounced the attempted attack on Monday.
"We condemn the latest Houthi missile attack on Abu Dhabi," said Ned Price, spokesman for the US Department of State.
"While Israel’s president is visiting the UAE to build bridges and promote stability across the region, the Houthis continue to launch attacks that threaten civilians," he said.