"The ICRC appeals for essential health services to be restored," it said in a statement.
"It reminds medical personnel that it is their duty as a matter of medical ethics to provide such services, and urges the international community to seriously consider the consequences in humanitarian terms of funding to the Palestinian Authority."
Hospitals in the West Bank are operating at one-fifth of their capacity and many small medical facilities are completely closed because of the suspension, the ICRC said.
The ICRC said that international humanitarian law made Israel, as the occupying power, responsible for ensuring the basic needs of Palestinian civilians were met, and implicitly urged Israel and Western countries to rethink their suspension of funding to the Palestinian Authority (PA).
Economic sanctions were imposed on the PA after the rise of Hamas in the January elections.
The present health care crisis had been worsened by strikes - over non-payment of salaries - by ministry of health staff working for the territories' main health services provider.
"Emergency life-saving services as well as curative and preventative care are jeopardised by the current situation," the ICRC added.
The ICRC cited the death on Monday of a young girl with acute fever who was turned away by a local hospital because of the strike and could not get access to private clinics because her parents could not afford the fee.