In a statement carried by Saudi media, the coalition said the oil tanker was in worldwide waters when it came under "Houthi-Iranian attack" at around 1330 local time (1030 GMT).
Yemen has been hit by many air strikes.
The media department of the Houthi-run Yemeni military said naval forces had "targeted a battleship belonging to the coalition in response to the bombardment of displaced people in Hodeidah".
"While this is ongoing, it would be inappropriate to comment further".
The United Nations asked donors on Tuesday for almost $3 billion to help an estimated 13 million people who urgently need aid in war-ravaged Yemen. The operation of the port, controlled by the Iran-aligned Houthis, was not affected by the air strike.
The Houthi rebels have intensified attacks against Saudi Arabia in recent weeks following the third anniversary of the war in Yemen.
MI and Villanova close out March Madness tonight
The 2017-18 college basketball season is down to its final day, and only two teams are left standing: Villanova and MI . It's also worth noting that Villanova has a top-15 rated defense, and is pretty adept at shutting other teams down.
Workers said the warehouses also contained hundreds of thousands of mattresses meant for those displaced by the war, which has killed more than 10,000 people and crippled the economy. Sustaining minor damage, the oil tanker completed its course accompanied by the coalition ship, Al Arabiya reports.
At the end of a year ago, the Houthis threatened that they would start attacking oil tankers and warships sailing under enemy flag if the Gulf coalition fighting it in the country does not reopen its ports. Debris from the missiles fell on a home, killing one person.
"No coalition member can claim clean hands in Yemen until all its members explain their role in scores of documented unlawful attacks", said Sarah Leah Whitson, Middle East director at Human Rights Watch, last year.
Tensions have been rising in recent days after the Houthis, who control most of northern Yemen, launched a series of missile strikes on Saudi Arabia, including the capital Riyadh, in recent days.
"But just as unlawful coalition air strikes don't justify the Houthis' indiscriminate attacks, the Saudis can't use Houthi rockets to justify impeding life-saving goods for Yemen's civilian population". The United Nations said that blockade raised the danger of mass starvation, and it was partially lifted.