The attack, which sent US troops into bunkers, was the second in a week on the UAE, the tourism and commercial hub of the Gulf region. On January 17, the Houthis hit a fuel depot in Abu Dhabi, killing three people.
The Houthis, battling a Saudi-led military coalition that includes the UAE, have said they aim to punish the Gulf state for backing militias that are blocking their attempts to capture oil-producing regions in Yemen.
A Houthi military spokesperson said the group had fired Zulfiqar ballistic missiles at al-Dhafra airbase, used by US forces, and other "sensitive targets". He said it had also launched drones towards Dubai.
"We advise foreign companies and investors in the UAE to leave as it has become unsafe," he said, adding the group was ready to "meet escalation with escalation".
The foreign ministry of the UAE, part of the six-nation Gulf Cooperation Council (GCC), called the attack a "criminal escalation" and said it had a right to respond.
The US military said it had fired multiple Patriot missile interceptors at two inbound missiles, and acknowledged simultaneous efforts by UAE's military.
"The combined efforts successfully prevented both missiles from impacting the base," said a spokesperson at US Central Command who represents US forces in the Middle East.
The Emirati ambassador to Washington, Yousef al Otaiba, tweeted that close cooperation with the United States had helped to deflect the attack, and the US State Department reaffirmed Washington's commitment to strengthen the defences of its Saudi and Emirati partners.
The Houthis have repeatedly carried out cross-border missile and drone attacks on Saudi Arabia, but by targeting the UAE they have raised the stakes of a conflict largely seen as a proxy war between Saudi Arabia and Iran.
Air strikes on Yemen, which the Saudi-led coalition says are aimed at crippling Houthi capabilities, killed at least 60 people in Saada province on Friday, and about 20 people in the Houthi-held capital Sanaa on Tuesday.
The US embassy issued a rare security advisory for the UAE, urging its citizens to "maintain a high level of security awareness".
"This is absolutely an escalation and changes the regional dynamic," said Karen Young, director at the Middle East Institutes' Economics and Energy Programme.
