"Let us be clear. Those using ever more destructive weapons know exactly what they are doing. They know they are committing war crimes," Ban told the Security Council.
"Imagine the destruction. People with limbs blown off. Children in terrible pain with no relief," he said. "Imagine a slaughterhouse. This is worse."
The two biggest hospitals in rebel-controlled parts of Aleppo have been bombed in what non-governmental organisations and residents say are deliberate attacks by the Syrian regime and its Russian allies to eliminate these structures.
In a statement, UNICEF said at least 96 children have been killed and 223 wounded in the rebel-held sections of the city since Friday. It said the health system was crumbling with only 30 doctors left to treat the wounded.
In May, the UN Security Council adopted a resolution on the protection of health workers and facilities during armed conflicts, but there has been no letup in these kinds of attacks in Syria and Yemen.
"International law is clear: medical workers, facilities and transport must be protected. The wounded and sick -- civilians and fighters alike -- must be spared," Ban said.
"Deliberate attacks on hospitals are war crimes. Denying people access to essential health care violates international humanitarian law."
He addressed ambassadors from the 15 UN Security Council members in a meeting focused on medical aid to civilians in conflicts.
He reminded them of a series of recommendations that have been made to prevent and stop attacks on medical facilities and for impartial and systematic investigations of any incidents that arise.
Ban cited statistics gathered by Physicians for Human Rights that show that 95 per cent of the medical personnel who were in Aleppo before the war "have fled, been detained, or killed."
"There must be action. There must be accountability," he said.
Joanne Liu, international president of Doctors Without Borders, asked Ban to name a special representative with a mandate to document and report on attacks on medical facilities, health workers and patients, stressing "impunity must end.