"At dawn, six buses of IS fighters and their relatives left the Yarmuk Palestinian refugee camp and adjacent district of Tadamun," said Rami Abdel Rahman, head of the Britain-based Syrian Observatory for Human Rights.
Abdel Rahman said the buses headed east for Syria's vast desert, where IS still controls some territory.
He had no details on how many people were aboard the vehicles, but said a majority of them were relatives of jihadists and not armed.
The evacuations came a day after an apparent deal was reached to put an end to a ferocious month-long offensive to oust IS from its last positions in southern Damascus.
Pro-regime forces, specifically Palestinian militias, had been fighting since April 19 to recapture Yarmuk, Tadamun, and the nearby districts of Qadam and Hajar al-Aswad from IS.
The assault had killed more than 250 pro-regime forces and another 233 IS fighters, according to the Observatory.
Fighting died down around midday on Saturday amid reports that an evacuation deal could be reached.
Syrian state media on Sunday denied evacuations were taking place in Hajar al-Aswad, but did not mention departures from Yarmuk or Tadamun.
Once a thriving district home to some 160,000 Palestinians and Syrians, Yarmuk's population has fallen to just a few hundred people.
