The clashes broke out on Sunday in Yarmouk, where 20,000 people have been trapped for months by Syria's civil war and are dependent on humanitarian supplies delivered by UNRWA, the UN agency which supports Palestinian refugees.
The Syrian Observatory for Human Rights, a Britain-based monitoring group, said an ambulance driver was killed in mortar fire on Sunday and residents reported several explosions.
A Palestinian group that supports President Bashar Assad, the Popular Front for the Liberation of Palestine-General Command, blamed the fighting on al Qaeda's Syrian branch, the Nusra Front.