Houthi forces have fired such missiles at ships previously.
I lived the best years of my life in Hodeidah where I went to high school.
He added that Saudi-led helicopters rushed to save the forces aboard the vessel, which is now burning near Yemen's coastline.
"The enemy has heightened the risk in the Red Sea with this new battle and is responsible for the consequences".
They say a network of minefields in the rebel-held areas has hindered the advance of government forces. The port is some 150 kilometers (90 miles) southwest of Sanaa, Yemen's capital held by the Houthis since they swept into the city in September 2014.
Emirati Minister of State for Foreign Affairs Anwar Gargash earlier told French newspaper Le Figaro the deadline for a withdrawal from Hudaida by the Houthis expired early on Wednesday morning.
The United Nations on Monday withdrew its worldwide staff from Hodeida, saying an attack would "impact hundreds of thousands of innocent civilians".
The assault marks the first time the Arab states have tried to capture such a heavily-defended major city since joining the war three years ago against the Iran-aligned Houthis, who control the capital Sanaa and most of the populated areas. It includes Emirati and Sudanese troops as well as Yemenis, drawn from southern separatists, local Red Sea coast fighters and a battalion led by a nephew of late ex-president Ali Abdullah Saleh.
Over 10,000 people have been killed in Yemen's civil war, which has displaced 2 million more and helped spawn a cholera epidemic.
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Saudi-led coalition warplanes and Apache helicopters provided "continuous" air support to pro-government forces, striking Huthi positions, military sources said.
According to Houthis, their forces repelled the attack and managed to destroy a Saudi-led coalition warship using two missiles.
"The battle for Hodeidah will nearly certainly result in a huge loss of civilian life and damage to vital infrastructure", said Tamer Kirolos, Yemen Country Director for Save the Children.
The United Nations is struggling to avert disruption to the port, the main lifeline for food aid to a country where 8.4 million people are on the verge of starvation, potentially the world's worst famine for decades.
Last month, the committee advanced legislation making U.S. midair refueling contingent on Saudi and Emirati efforts to engage in diplomacy, ensure access of humanitarian goods, reduce civilian casualties and avoid damaging critical infrastructure. "We are there and delivering, we are not leaving Hodeidah", said Lise Grande, U.N. humanitarian coordinator for Yemen.
In a tweet, the UN's envoy to Yemen, Martin Griffiths, called on both sides to end the fighting and find a negotiated settlement.
Foreign Secretary Boris Johnson said on Wednesday the British government was in contact with the alliance about ensuring its operations comply with worldwide law on protecting civilians.
A major battle in Hudaydah has potentially grave implications for the already-dire humanitarian situation in Yemen. Effort to kill Trump tariffs blocked Trump stokes confusion with pledge to halt Korean war games Five takeaways from Trump's summit with Kim Jong Un MORE and Secretary of State Mike PompeoMichael (Mike) Richard PompeoWith caveats, Republicans praise Trump's summit with Kim Jong Un Pavlich: Pompeo: The man for the job on North Korea Five takeaways from Trump's summit with Kim Jong Un MORE on the eve of the offensive expressing "grave alarm".
"We do not provide any additional support to the Saudi coalition's military operations", he said.