Eleven clinics have already been shut in Darfur, Blue Nile and South Kordofan where years of fighting between government troops and black African rebels has forced tens of thousands of people to flee their homes.
As an acute cash crunch worsens and with the world's eyes focused on other conflicts such as Syria, another 49 facilities in these regions are also at risk, the WHO head in Sudan, Naeema al-Gasseer, told AFP.
"About 11 clinics have already been closed and another 49 are facing closure.
"We are talking about a million people who can be affected."
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The closures could impact immunisation services, while some 323,000 women of child-bearing age and children under five will lack access to health care, she said.
"A heightened risk of epidemics is likely... With people having to travel long distances to access available health care services," Gasseer said.
WHO, a United Nations agency, needs about $7 million to operate these clinics over the next year, but is having trouble sourcing the funds.
Violence broke out when ethnic minority rebels rose up against President Omar al-Bashir, accusing his Arab-dominated government of marginalising the region.
Similar fighting has also plagued Blue Nile and South Kordofan, with tens of thousands of people killed or displaced in these three areas in more than a decade.
Funding for Sudan's health care sector has fallen in the past two or three years.
The cash crunch faced by WHO and other NGOs is so severe that many clinics have no money even to buy medicines or to pay staff wages.
"We don't have funds... To maintain the equipment or for food for malnourished children."
Save the Children Sweden is phasing out health and nutrition services in 20 centres in South Kordofan, affecting about 200,000 people who it has supported.