The UN plane brought the children and nine relatives to the Jordanian capital Amman on Monday following their evacuation, reports Efe news.
The children are suffering from cancer, kidney disease or need organ transplants or reconstructive surgery.
The international airport in Yemen's capital Sanaa has been closed to commercial flights amid an airspace blockade that began in 2016.
"We hope that all of the patients who need medical treatment are allowed to leave the country. That's our aim. This is the first of what we hope to be many flights," the UN's resident coordination officer in Yemen, Lise Grande, told Efe news.
"This is the first flight of the medical air bridge. They are patients who are suffering from conditions and diseases that can't be treated here in Yemen. They are to be taken to Jordan where they are going to receive the assistance they need in order to survive."
The UN and the World Health Organization have been working almost two years to establish the "air bridge", Grande said.
Sanaa is under the control of the Houthis, an Iran-aligned rebel group opposed to the internationally recognized government of Abdu-Rabeh Mansour Hadi.
The airspace is in the hands of the pro-Hadi Arab coalition and has remained closed to civilian craft since 2016.
Houthi health authorities say that around 32,000 patients need to be airlifted via Sanaa airport for medical treatment abroad.
Yemen has been bogged down in a brutal civil war for the last five years.
A Houthi uprising that forced Hadi to move to Aden was met with a Saudi Arabia-led aerial campaign.
( With inputs from IANS )