The last UN food aid to reach Taiz, Yemen's third city, was more than five weeks ago when food was distributed to nearly 240,000 people, it said.
"We plead for safe and immediate access to the city of Taiz to prevent a humanitarian tragedy as supplies dwindle, threatening the lives of thousands - including women, children and the elderly," WFP regional director Muhannad Hadi said in a statement reported by Reuters.
"These people have already suffered extreme hunger, and if this situation continues the damage from hunger will be irreversible."
On Wednesday, warplanes from the Saudi-led coalition bombed the Houthi positions across Yemen and dropped weapons to militias in Taiz, situated in the southwest.
Ten of Yemen's 22 governorates were assessed as being in an emergency food situation in June, one step below famine on a five-point scale. The assessment has not been updated since then, partly because experts have not managed to get sufficient access to survey the situation.
About a third of the country's population, or 7.6 million people urgently require food aid, the WFP said.
On March 26, a coalition spearheaded by Saudi Arabia began deadly airstrikes against the Houthi movement in an attempt to restore power to the fugitive former President Abd Rabbuh Mansour Hadi, a close ally of Riyadh.
More than 5400 people, many of them children and women, have been killed in the Saudi-led aggression against the already impoverished Arab country so far.
The Saudi-led aerial strikes have targeted 61 hospitals and 13 ambulances.