The ship, carrying military equipment, was arriving at Yemen's Mocha port from Eritrea's Assab port when it was attacked, Houthi officials said on Saturday.
The Saudi Press Agency, citing a statement by the coalition, said that Houthis used an explosives-laden boat, which struck the pier close to a group of ships at Mocha.
It added that there were no casualties or any substantial damage.
UAE vessel is the third ship belonging to the coalition to be attacked off Yemen's western coast since the beginning of 2017, according to AP news agency.
Also on Saturday, Yemeni officials said that forces loyal to President Abd-Rabbu Mansour Hadi took full control of a key military base, known as Khalid Ibn al-Walid, near Yemen's west coast.
Clashes that raged over the base between forces loyal to Hadi and Houthis, who controlled it for more than two years, have killed dozens on both sides.
Later on Saturday, other Yemeni officials said that 13 of Hadi's forces were killed after Houthis attacked a military site south of the city of Taiz, on the southwest coast.
They said that five Houthis were killed in the clashes and expected the death toll among Hadi's forces to rise.
The Saudi-led coalition, backing Hadi's internationally recognised government, has waged an air campaign since March 2015, seeking to dislodge the Houthis, who seized the capital Sanaa and other areas in 2014.
The coalition, mostly of Sunni Arab countries, aims to restore Hadi back to power.