About 30 staffers from Leer Hospital were trying to care for severely ill patients in the bush, MSF or Doctors Without Borders said. Ambulatory patients fled the hospital on their own.
Raphael Gorgeu, the MSF head of mission, said Leer is the only functioning hospital in Unity State.
Its closure deprives 270,000 people of medical care.
"Despite incredibly challenging circumstances, MSF local staff continued running the hospital in Leer for as long as they could," Gorgeu said. "However in the past three days, the situation became too unstable and the only way to provide medical care was to take patients out of the hospital and to flee with the population into the bush."
The United Nations announced Thursday it has increased patrols in South Sudan. The United Nations Mission in South Sudan, or UNMISS, has 12,500 soldiers and 1,323 police in the country.
Violence has been a problem since South Sudan became independent in 2011. It increased following a December military mutiny, described by President Salva Kiir as an attempted coup.
The United Nations estimates 100,000 people have become refugees because of the fighting, many of them fleeing across the borders to neighboring countries.