Israel has prohibited the entry of fuel as part of tightened restrictions
The United Nations has warned supplies of emergency fuel for critical facilities in Gaza are running out.
The fuel is being provided by the UN.
Jamie McGoldrick, humanitarian coordinator for the Occupied Palestinian Territory, said: "At least one hospital has been forced to shut down for a few hours, and services are being dramatically reduced at others.
"Given ongoing blackouts of about 20 hours a day, if fuel does not come in immediately, people's lives will be at stake, with the most vulnerable patients, like cardiac patients, those on dialysis, and newborns in intensive care, at highest risk."
The humanitarian situation in Gaza, controlled by Hamas, has been negatively impacted by a blockade of the enclave imposed by Israel.
Since last Monday, Israeli authorities have prohibited the entry of fuel into Gaza as part of tightened import and export restrictions - reportedly in response to the launch of incendiary kites from Gaza into Israel.
Mr McGoldrick has called on Israel to end restrictions preventing the import of fuel, and for donors to provide immediate funding for emergency fuel, currently set to run out in early August.
According to the World Health Organization (WHO) Al Quds Hospital, which provides life-saving medical interventions for 150,000 people per year - including major surgeries, deliveries and intensive care - will be forced to shut down in coming days.
Four other hospitals are also set to run out of fuel within the next three days.
The Palestinian Ministry of Health has already implemented strict contingency measures: hospitals have reduced diagnostic, sterilization and cleaning services, increasing the risk of infections amongst patients.
Elective surgeries are being further reduced.
Over 7,000 elective surgeries have been postponed in recent months due to the mass trauma casualties and low resources available to cope with the demand.
At highest risk are over 2,000 patients in Gaza's hospitals who rely on electrical devices, including newborns in incubators.
The UN says over 1.27 million people would be directly affected by hospital closures and a reduction in the provision of vital health interventions.
While reduced functioning of water and sanitation facilities risks an increase in waterborne disease and outbreaks.
Mr McGoldrick added: "Until more sustainable solutions for the electricity crisis in Gaza are found, two steps can avert further devastation in Gaza in the short term.
"Israel must let fuel and other essential supplies in and donors must mobilize resources to ensure that critical facilities receive the fuel they need."
An average of 950,000 litres is distributed by the UN each month to around 220 critical hospitals and health clinics, water and sewage treatment sites and solid waste collection services.