Houthi rebel leaders said on Tuesday that the radio navigation system at Sanaa International Airport had been destroyed in a Saudi airstrike.
"We have some 21 million people needing assistance and seven million of those are in famine-like conditions and rely completely on food aid", United Nations humanitarian coordinator for Yemen Jamie McGoldrick said.
Saudi Arabia announced on Monday that the Coalition Supporting Legitimacy in Yemen would begin gradually reopening airports and seaports in Yemen, days after closing them over a Houthi ballistic attack on Riyadh.
Jamie McGoldrick, the head of the UN's aid mission in Yemen, criticised the Saudis, saying such measures would take too long to implement and cause needless deaths.
Yemen's national airline said on Tuesday a commercial flight had landed at Aden global airport after acquiring security permits.
The announcement from the Saudi mission at the United Nations came after the coalition fighting Yemen's rebels, known as Houthis, faced widespread global criticism over the closure, with the U.N. and over 20 aid groups saying it could bring millions of already suffering people closer to "starvation and death".
"The port at Aden does not have the capacity for commercial and humanitarian cargo, and unless the Red Sea ports in Hodeida and Saleef are opened immediately, the United Nations will not be able to feed 7 million people every month", said United Nations spokesman Stephane Dujarric.
After a November 4 ballistic missile attack near the Riyadh worldwide airport by Houthi rebels, Saudi Arabia had announced it shut down all ports in Yemen.
Aden port, which is controlled by allies of Saudi Arabia, does not have the capacity to handle the necessary volume of humanitarian cargo, he added.
Last week, the World Health Organization (WHO) warned that more Yemeni civilians would die because of the closure of the Yemeni ports.
More than 2,000 Yemenis have died in a cholera outbreak now affecting almost one million people.