The UAE military said a boat under its command was involved in an "incident" in the Bab al-Mandab strait. It said there were no casualties.
"Rockets targeted an Emirati warship as it approached the coast of Mokha" on the Red Sea, the Iran-backed Houthi rebels said in a statement on their sabanews.net website.
"It was completely destroyed," they said.
In a statement published by the official WAM news agency, the Emirati military said the boat was on a routine trip from Aden, further south, and that an investigation has begun.
It said the boat had been hired, but did not provide more details or say if the vessel was damaged.
The UAE is a key member of the coalition that has been battling Iran-backed Houthi rebels and their allies since March last year in support of President Abedrabbo Mansour Hadi's internationally recognised government.
Since March 2015, the coalition has pushed the rebels out of much of Yemen's south, but they still control nearly all of the country's Red Sea coast as well as swathes of territory around the capital Sanaa.
In the northern province of Jawf, pro-government forces on Saturday recaptured large parts of the town of Ghail after clashes that killed 11 rebels and five loyalists, military sources said.
Jawf is on the border with Saudi Arabia and is mostly controlled by loyalist forces.
In the Bab al-Mandab region itself, fighting on Saturday killed three loyalists and wounded 17, other military sources said.
The clashes took place in the mountainous Kahbub area overlooking the strait.
Five rebels were also killed, the loyalist military sources said.
AFP could not verify the rebel toll from independent sources, and the insurgents rarely acknowledge their losses.
Loyalist forces recaptured Perim island in the Bab al-Mandab strait in October last year, gaining a foothold on the strategic shipping lane which connects the Suez Canal and Red Sea with the Gulf of Aden and the Indian Ocean.
But the rebels still control some of the heights which overlook the strait from the mainland, where there has been fierce fighting in recent days.
Military sources in Yemen told AFP that the rebels shelled a loyalist military camp in the Bab al-Mandab area on Saturday.
More than 6,700 people, including civilians, have been killed in the Yemeni conflict since the coalition began its air campaign in March 2015, the United Nations says.
The UAE military said a boat under its command was involved in an ,incident, in the Bab al-Mandab strait. It said there were no casualties.
Yemeni rebels claimed on Saturday that they hit a vessel operated by the Emirati military, which is part of a Saudi-led coalition fighting in support of Yemen's government.
