A Houthi spokesperson told CNN the Iranian-allied group was responsible for Saturday's attack, which occurred as the vessel headed for the port city of Aden.
The Saudi-led Arab coalition, which has been fighting in support of the Yemeni government under President Abd Rabbuh Mansur Hadi, called the attack a "dangerous indication" and launched a rescue mission for those aboard the stricken ship.
The vessel, owned by the UAE's National Marine Dredging Company, was reportedly delivering medical aid and other supplies when it came under fire in the Bab al-Mandab Strait -- which lies between the southern tip of Yemen and Djibouti and Eritrea in the Horn of Africa -- according to the WAM report.
''This comes as a serious indicator to confirm the orientation of these militias to carry out terrorist operations targeting the international navigation and relief ships in Bab al-Mandab Strait," the coalition said in a statement posted on WAM.
'Legitimate target' claim
But Mohammed Al Bukhaiti, a spokesman for the Houthi fighters, said he did not believe the ship was carrying aid material.
"In any case, the Yemeni people consider the Emiratis and Saudis their enemies and so anything belonging to them is a legitimate target," said al-Bukhaiti, speaking to CNN by phone Sunday from the Yemeni capital, Sanaa, which is run by Houthi rebels since they seized it last year.
The Houthi-run Al Masirah TV published a video that purported to show the moment of attack. CNN could not independently verify the authenticity of the footage.
The southern port city of Aden functions as the de facto capital of the Saudi-backed Yemeni government after they were pushed out of Sanaa.
A Saudi-led coalition, which is made up of several Arab countries including the UAE, began a military campaign aimed at restoring the Yemeni government and preventing the Houthis and forces loyal to deposed President Ali Abdullah Saleh from taking power.
Sanaa has suffered some 45 airstrikes over the past 24 hours, according to multiple witnesses. That's the most intense barrage on Sanaa since last June, according to Yemeni Journalist Hakim Almasmari.
At this time there is no indication of a connection between the strike on the Emirati vessel and the Sanaa airstrikes.
At least 10,000 people have been killed in Yemen since the conflict began in March 2015, according to UN figures.
The violence has also displaced three million Yemenis and forced 200,000 to seek refuge abroad.