Aid agencies said that while their ground operations were broadly unaffected, they had seen a significant increase in demand as other facilities are unable to fully function.
Afghanistan's healthcare system is at risk of collapse, two major aid agencies told the news agency Reuters, after foreign donors stopped providing aid following the Taliban takeover.
After the United States withdrew the bulk of its remaining troops last month, the Taliban accelerated its military campaign, taking control of the capital Kabul on August 15.
International donors including the World Bank and European Union froze funding to Afghanistan shortly afterwards.
"One of the great risks for the health system here is basically to collapse because of lack of support," said Filipe Ribeiro, Afghanistan representative for Medecins Sans Frontieres (MSF), one of the largest medical aid agencies in the country.
"The overall health system in Afghanistan is understaffed, under-equipped and underfunded, for years. And the great risk is that this underfunding will continue over time."
Necephor Mghendi, Afghanistan head of the International Federation of the Red Cross and Red Crescent (IFRC), said the healthcare system, which was already fragile and heavily reliant on foreign aid, had been left under additional strain.
"The humanitarian needs on the ground are massive," he said.
Both aid agencies said that while their ground operations were broadly unaffected, they had seen a significant increase in demand as other facilities are unable to fully function.
Mghendi said closures of Afghan banks had meant almost all humanitarian agencies have been unable to access funds, leaving vendors and staff unpaid.
Compounding the issue, medical supplies will now need to be restocked earlier than expected.
"Supplies that were supposed to last for three months will not be able to last three months. We may need to replenish much earlier than that," Mghendi said.
Ribeiro said MSF had stockpiled medical supplies before the takeover but that with flights disrupted and land borders in disarray, it was unclear when more might reach the country.
The World Health Organization said on Monday that a plane carrying 12.5 tonnes of medicines and health supplies had landed at Mazar-i-Sharif in northern Afghanistan, the first such shipment since the Taliban took control.
During its period in power from 1996-2001, the Taliban had an uneasy relationship with foreign aid agencies, eventually expelling many, including MSF, in 1998.
This time, the group has said it welcomes foreign donors, and will protect the rights of foreign and local staff - a commitment that has so far been upheld, Ribeiro said.
"They actually asked us to stay, and they asked us to keep running our operations the way we were running them before," he said. "The relations are, so far, pretty reassuring."