The ICRC and the United Nations have been trying for days to get aid flights into the country, where warplanes from a Saudi-led coalition have carried out air strikes against Houthi fighters battling to take over the southern port city of Aden.
The fighting has killed more than 600 people.
ICRC spokeswoman in Yemen, Marie Claire Feghali, speaking by telephone from Sanaa airport, said the Red Cross shipment included 16.4 tonnes of medicines, bandages, intravenous drips and surgical equipment.
UNICEF spokesman Christophe Boulierac said the U.N. agency`s plane had also landed after a week of delays. "Our plane has just landed in Sanaa from Djibouti," he said.
Aden residents say electricity and water have been cut off in several districts, rubbish has been left uncollected in the streets and hospitals have been unable to cope. (Reporting by Dominic Evans in Dubai and Stephanie Nebehay in Geneva; Editing by Louise Ireland)
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