The Islamic State has taken control of large parts of the Palestinian camp after violent clashes between groups inside the camp and the militants, according to officials.
Unrwa, a UN relief agency for Palestinian refugees, said that the fighting would put Yarmouk's civilians, including large numbers of children, "at extreme risk of death, serious injury, trauma and displacement".
It is seeking an end to the conflict and "a return to conditions that will enable its staff to support and assist Yarmouk's civilians".
Anwar Abdel Hadi, director of political affairs for the Palestine Liberation Organisation in Damascus, told AFP that "fighters from ISIL launched an assault this morning on Yarmouk and they took over the majority of the camp" on Wednesday.
The Syrian Observatory for Human Rights said ISIL was in control of a "large part" of the neighbourhood after fighting with Palestinian groups also against President Bashar al-Assad's regime.
An activist in Yarmouk told Al Jazeera that IS fighters - from the neighbouring town of Hajr al-Aswad - stormed the western side of Yarmouk and seized areas from the Palestinian-armed group Bait al Maqdis.
He added that fighting has been continuing but denied reports that most of Yarmouk had been seized by ISIL.
"Parts of Yarmouk are being shelled, but it is unclear whether it is by regime forces or ISIL," he said.
The UN says about 18,000 Palestinian refugees are inside the camp.
Islamic militants have previously taken control of large areas in eastern Syria and across northern and western Iraq. But this is the group's first major attack near the heart of the Syrian capital – just 6.5km from Damascus.
Yarmouk residents told BBC Arabic that members of Aknaf Beit al-Maqdis, a group formed by Palestinian militiamen opposed to the Syrian government, were leading the fight against the IS militants, along with Free Syrian Army fighters.
Palestinian militiamen are fighting back and were able to retake some areas from IS later on Wednesday, residents told the BBC.