"What is unfolding in Yarmuk is unacceptable," Ban told reporters in New York.
"We simply cannot stand by and watch a massacre unfold."
Some 18,000 people are trapped in Yarmuk, which IS entered on April 1 and where it is battling Palestinians and Syrian rebels, and coming under increased regime shelling.
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.
"In the horror that is Syria, the Yarmuk refugee camp is the deepest circle of hell," Ban said, calling for the fighting to stop so aid can be delivered.
- 'Joint ops room' -
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.
It was unclear if Aknaf Beit al-Maqdis -- the key group battling IS inside Yarmuk -- would agree to fight alongside government forces.
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.
On Wednesday, the Syrian reconciliation minister discussed Yarmuk with Majdalani and suggested that Syrian troops could be involved in an assault on IS there but that the government would decide.
"The priority now is to expel and defeat militants and terrorists in the camp. Under the present circumstances, a military solution is necessary," Haidar said.
The government and residents of the capital have been rattled by the IS presence just a few kilometres (miles) from the heart of Damascus.
- 'Soldiers beheaded' -
The IS advance into Yarmuk has sparked international concern and warnings from rights and aid groups that life in the camp has become more desperate then ever.
Residents who have managed to flee Yarmuk spoke this week of horrors committed by IS militants.
"I saw severed heads. They killed children in front of their parents. We were terrorised," said Ibrahim Abdel Fadel who fled with his wife and seven children.
IS, which has seized chunks of Syria and Iraq, has a reputation for carrying out atrocities.
On Thursday, IS beheaded three Syrian soldiers after attacks in the central province of Homs that left 17 soldiers and pro-regime fighters dead, said the Syrian Observatory for Human Rights.
On the political front, talks hosted by Russia between the Syrian government and members of the tolerated opposition dragged on Thursday with little sign of concrete progress.
More than 215,000 people have been killed in Syria since the conflict began in March 2011 with anti-government protests which spiralled into war after a regime crackdown.