At least 560 people, including dozens of children, have been killed, mostly in a Saudi-led air campaign and battles between Shiite rebels and forces loyal to the embattled president.
More than 1,700 people have been wounded and another 100,000 have fled their homes as fighting intensified over the past three weeks, the World Health Organization said.
The Red Cross shipment would be the first to reach Yemen since the start of the Saudi-imposed air blockade. Sitara Jabeen, a Geneva-based spokeswoman for the International Committee of the Red Cross, said a cargo plane with 17 tons of medical supplies was in the Jordanian capital, Amman, awaiting the go-ahead from coalition forces to land in Sanaa, hopefully on Wednesday. Another 35 tons of supplies were also ready for shipment, she said.