"We are not planning to destroy the infrastructure," Foreign Minister Khaled Alyemany said.
Pro-government forces, backed by a Saudi-led coalition, began an assault on the Red Sea city on Wednesday.
Aid agencies have said the battle threatens to cut off basic supplies to millions of people at risk of famine.
On Friday, pro-government fighters advanced on Hudaydah's airport with the support of coalition air strikes on positions held by the rebel Houthi movement.
At a news conference in New York on Thursday, Mr Alyemany said: "We are in an area close to the airport, but not to the seaport.
"The seaport is totally out of operations, today," he added.
The UN's World Food Programme said the seaport was still operational, and that its staff were still working and distributing food.
Executive Director David Beasley urged all parties "to meet their obligations to protect civilians and civilian infrastructure and take active steps to respect international humanitarian law".
Coalition warplanes have frequently bombed Hudaydah's port over the past three years despite its importance to humanitarian operations. A partial coalition blockade of Hudaydah has also significantly reduced imports of essential goods.
As ever, there are two conflicting versions of events on the ground on Hudaydah.
Upbeat statements here in the Gulf talk of the coalition reaching the airport and of relentless pounding of Houthi defensive positions south of the city. But the Houthi rebels appear to be digging in for a long haul and are calling for reinforcements to defend Hudaydah from the advancing pro-government troops.
Unless the Houthis capitulate and withdraw their forces from the city, the coalition will be forced to decide whether to risk going into the city and fighting street by street, or waiting it out on the outskirts with a prolonged siege. Either scenario is likely to see further suffering for Yemen's impoverished population.
But for Saudi Arabia, the United Arab Emirates and the Yemeni government, Hudaydah is a prize they cannot afford to give up on. Their strategic goal is to force the Houthis out of it, thereby depriving them of their main source of revenue and compelling them to sue for peace.
The UN Security Council met in a closed-door session on Thursday, amid fears that the fighting could result in thousands of civilian casualties and trigger a wider humanitarian crisis.
Ahead of the talks, Sweden's permanent representative Carl Skau said it was time for the council to call for an immediate freeze to the assault on Hudaydah. There was, however, not enough support among council members.
Instead, they "reiterated their call for the ports of Hudaydah and Saleef to be kept open", according to Russian permanent representative Vasily Nebenzia, who holds the council presidency.
Mr Nebenzia said the council members were "united in their deep concern about the risks to the humanitarian situation".
Rebel leader Abdul Malik al-Houthi meanwhile urged his supporters to mobilise to defend Hudaydah, threatening to turn the area into a "quagmire" for pro-government forces.
Heavy fighting has been reported since the offensive began two days ago, with Houthi positions coming under attack from coalition warships and aircraft.
Medical sources quoted by AFP news agency said 30 Houthi rebels were killed on Thursday along with nine pro-government soldiers.
Meanwhile, Saudi-owned news channel Al Arabiya said Yemeni President Abdrabbuh Mansour Hadi had returned to the temporary capital of Aden to oversee the battle for Hudaydah.
"The hour of victory is close and the return of justice is nearing that will lead to the triumph of the will of the Yemeni people," he was quoted as saying on arrival.
Mr Hadi has spent much of his time in neighbouring Saudi Arabia since rebels seized control of Sanaa and then launched an assault on Aden in March 2015.
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