"They will be transported to the United Arab Emirates for treatment," the source, who requested anonymity because they are not authorised to speak to the media, told AFP.
It is the first evacuation from Gaza since the Rafah border crossing was closed in early May, when Israeli forces took over the Palestinian side of the terminal.
Negotiations to re-open the Rafah crossing, a key conduit for aid and evacuations, have repeatedly floundered.
Cairo has refused to resume operations through the crossing as long as Israeli forces remain in control of the Palestinian side.
Some aid trucks have been diverted to the nearby Kerem Shalom crossing with Israel, but humanitarian sources say the daily average of trucks entering the Palestinian territory have been less than 90 a day.
The United Nations says a daily minimum of 500 trucks are needed to meet Gazans' basic needs.
The UN has repeatedly sounded the alarm on the humanitarian crisis in famine-stricken and bombarded Gaza, where the few remaining hospitals are struggling to function as food and other essentials become increasingly difficult to obtain.
At least 37,765 people have been killed in Gaza during more than eight months of war, according to the health ministry in the Hamas-run territory.
The Gaza war started with Hamas's October 7 attack on southern Israel that resulted in the deaths of 1,195 people, mostly civilians, according to an AFP tally based on Israeli official figures.
Palestinian militants also seized about 250 hostages, 116 of whom remain in Gaza, including 42 the Israeli army says are dead.
sar-bha/dv