The Yarmuk camp has been largely under the control of Syrian opposition forces for months and government forces have imposed a siege and choked off the entry of supplies into the camp since September.
"The evacuation has begun of a number of critical humanitarian cases from the Yarmuk camp," said Palestine Liberation Organisation official Anwar Abdul Hadi.
He added that 50 people had left the camp so far, and that "it is expected that by the end of the day around 100" people will have been evacuated.
Abdul Hadi said the evacuations would continue daily until 600 residents in a critical condition, along with those suffering chronic illnesses and children and pregnant women, had left Yarmuk.
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He also said that a new aid convoy carrying some 400 food packages was expected to enter the camp on Sunday.
His announcement comes the day after a first batch of food aid entered the besieged refugee camp, after an agreement was reached between representatives of Palestinian factions and rebels inside the camp.
On Friday, UN human rights chief Navi Pillay warned that blocking "humanitarian assistance to civilians in desperate need may amount to a war crime".