South Sudan 'preventing aid to Jonglei victims'
They do not have access to safe drinking water, food or medical care, Medecins Sans Frontieres (MSF) said.
South Sudan says Khartoum backs several rebel groups - charges it denies.
In turn, Sudan says the South supports militias on its territory.
Jonglei state has been hit by widespread ethnic violence since South Sudan became independent from Sudan in July 2011, with much of it taking place in Pibor county.
Earlier this week, South Sudanese President Salva Kiir said that it was difficult to differentiate between civilians and rebels in Jonglei state.
He accused the rebels of using civilians as human shields.
MSF says the only two hospitals in the whole of Pibor county have been looted and vandalised in the recent fighting, so there is no healthcare available for any of the displaced people apart from a basic MSF health post in Gumuruk.
"Immediate action is required to avoid catastrophe," Bart Janssens, MSF's director of operations, said in a statement.
"The area in Pibor county where the population is hiding will flood during the imminent rainy season.
"This will not be a place where people can remain alive."
He said that from the charity's years of experience of Jonglei it knew that without medical care mortality rates would rise rapidly, with people dying of pneumonia and other respiratory diseases, malaria and diarrhoea.
Repeated requests by MSF to the authorities to travel to the area where people are hiding in the bush have been denied, the charity said.
Following decades of conflict with Khartoum, South Sudan is among the least developed countries in the world.
The rebel group led by David Yau Yau, which is involved in the recent clashes in Jonglei state, has attracted support from youths of the Murle ethnic group.
The Murle are believed to have been angered by the activities of South Sudanese troops stationed in the area, who are mainly drawn from the rival Nuer community.
The two ethnic groups often clash over cattle, leading to deadly vendettas.