"First @ICRC flight reached Sanaa," " Dominik Stillhart, director of operations at the Red Cross, posted on his Twitter account.
"More to come by air and sea when clearances received to bring urgently needed medical supplies."
ICRC spokeswoman Sitara Jabeen said the first flight was a small passenger plane carrying medical staff and that it landed on Monday.
A cargo plane with medical supplies was waiting in Amman, she said.
"This plane will go to Sanaa tomorrow," said Jabeen.
The organization was also planning to send another aid shipment with a plane that would travel from Geneva to Sanaa.
Relief workers have warned of a dire situation in the impoverished country, where a Saudi-led coalition is waging an air war on the Iran-backed Huthi Shiite rebels.