About 7 million people face starvation in Yemen and their survival depends on global assistance.
The UN children's fund UNICEF said Saturday's flight was carrying more than 15 tonnes, or 1.9 million doses, of vaccine for diphtheria, tetanus and other preventable diseases.
"The needs are huge and there is much more to do for #YemenChildren", the world body said on its Twitter account.
"Sanaa airport was closed from November 6 until today, more than 18 days and this closure caused an obstruction to the presence of aid workers", Shayef told Reuters television in Sanaa.
But he warned that Saturday's aid delivery was not enough and demanded access to Sanaa airport for all flights in order to "save the lives of the sick", the rebel-run Saba news agency reported.
A spokesman for the US-backed coalition said in a statement issued on Friday that 82 permits have been issued for worldwide aid missions since November 4, both for the Sanaa airport and Hodeidah, the country's main port where some 80 per cent of food supplies enter.
The Arab Coalition in Yemen announced on Friday that 42 permits were issued for ships and relief aircrafts.
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Officials at the port said on Saturday that no ships have arrived yet and they were not expecting any to dock soon.
Yemeni Minister of the Local Administration Abdul Raqib Fatah had called on United Nations agencies to deliver relief and humanitarian aid to all of the country's provinces through ports and airports.
The missile was intercepted near Riyadh's King Khalid International Airport, sparking a war of words between Tehran and Riyadh, which accused Iran of "direct aggression" and supplying arms to the Houthis.
The United States called on the worldwide community to take the necessary steps to "hold the Iranian regime accountable for its repeated violations of United Nations Security Council Resolutions 2216 (adopted in 2015) and UN resolution 2231 as the Iranian Islamic Revolutionary Guard Corps exploits the grave humanitarian crisis in Yemen to advance its regional ambitions".
The UN says a continuation of the two-week blockade would make Yemen's war-battered population more vulnerable to cholera and starvation.
The Saudi-led coalition is fighting the Iran-backed Houthi rebels, who seized control of Sana'a in late 2014 and have since taken over other parts of the impoverished country.