Stephen O'Brien, who heads the United Nations humanitarian office (OCHA), issued a fresh plea to ease the suffering of some 250,000 people besieged by a Russian-backed Syrian government offensive to retake the key city.
In a statement, O'Brien called for "urgent action to bring an end to their living hell."
Syrian President Bashar al-Assad is battling to reclaim Aleppo, once the country's economic powerhouse. Diplomatic efforts to stem the bloodshed have failed.
"The healthcare system in eastern Aleppo is all but obliterated," O'Brien said, after the largest hospital in the rebel-controlled area was hit by barrel bombs on Saturday.
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"Medical facilities are being hit one by one," he added.
O'Brien urged warring parties to at the very least allow medical evacuations for the hundreds of civilians in urgent need of care.
The UN has said that water and food supplies in eastern Aleppo are running low, while efforts to bring in aid convoys through the Turkish border have been stalled by the fighting.
The UN had hoped it could restock east Aleppo during a ceasefire negotiated last month by the United States and Russia, but security conditions to allow those deliveries were not met and the ceasefire quickly collapsed.
With many basic medications now unavailable most supplies are running short, patients are being turned away from health centres and the need for evacuations is likely "to rise dramatically in the coming days," O'Brien said.
The battle for Aleppo has sparked some of the most brutal violence since the beginning in March 2011 of Syria's conflict, which has killed more than 300,000 people and displaced over half the population.