The World Food Programme (WFP) said it was "extremely concerned about the series of security incidents in Hodeida city these past few days in and around de-conflicted sites critical for the humanitarian response in Yemen", describing the situation as "alarming", AFP reported.
The UN agency warned that "the conflict (is) threatening the continuity of humanitarian assistance to the city and surrounding areas where needs are among the highest in the country."
Fighting has raged in recent days close to the Houthi-held port city, a crucial entry point for aid that the Saudi-led coalition has imposed a blockade on.
Alongside the threat of combat, civilians also face severe shortages of food, water and medicine in Hodeida province, according to the UN.
In August, WFP said it had provided emergency food assistance to some 700,000 of the around 900,000 people in the province considered to be at severe risk.
Agency spokesman Herve Verhoosel decried that a number of security incidences had been reported since Wednesday, including at the Red Sea Mill Silos, which mill a quarter of the agency's monthly wheat requirements in Yemen.
"The ongoing clashes could jeopardize the shipments of 46,000 tons of wheat expected to arrive to Hodeida within the next ten days," Verhoosel told reporters in Geneva.
Clashes near the mill "could impact our ability to feed up to 3.5 million very hungry people in northern and central Yemen for one month," he warned.
He said that a mortar shell launched by an unidentified armed group had also hit a WFP warehouse in Hodeida city "holding enough food to assist 19,200 very hungry people."
That attack injured a guard at the warehouse, he added.
Fighting has also been reported "in extremely close proximity" to WFP's offices and housing, Verhoosel said.
This, he said, "could potentially compromise the safety and security of 33 WFP staff in Hodeida city currently working round the clock to assist Yemenis suffering from acute hunger and malnutrition."
He said the agency was doing everything possible "to ensure the safety and security of our staff".
Nearly 15,000 people have been killed in Yemen's conflict since 2015, when the Saudi-led alliance invaded to reinstate the deposed government.