His appeal came as 14 Palestinian factions meeting in Damascus said they would back a joint military operation with Syrian government forces against the jihadists.
Syria's Reconciliation Minister Ali Haidar on Wednesday said the crisis required a military operation to expel IS from the camp in southern Damascus.
"What is unfolding in Yarmuk is unacceptable," Ban told reporters in New York.
"We simply cannot stand by and watch a massacre unfold."
The sprawling district, once home to 160,000 Syrians and Palestinians, has been devastated and endured a suffocating Syrian army siege since 2013.
Rights organisations say the blockade has led to deaths because of food and medicine shortages, and that the situation now is worsening.
"A refugee camp is beginning to resemble a death camp," Ban warned.
The refugees, including 3,500 children, have been "turned into human shields", with armed fighters inside the camp and government forces outside, he said.
Earlier, 14 Palestinian factions met in Damascus with Palestine Liberation Organisation official Ahmed Majdalani, who said they backed a joint anti-IS operation with Syrian regime forces.
"We agreed that there would be permanent cooperation with the Syrian leadership and the formation of a joint operations room with Syrian government forces and the Palestinian factions that have a significant presence in the camp or around it."
The PLO official gave no further details and it was not immediately clear when such a operation could begin or who would take part.
The anti-regime group did not attend Thursday's meeting.
Majdalani said Palestinian backing for a military operation was dependent on any action protecting civilian lives and infrastructure in the battered camp.
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