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The medical charity says as many as four young children die at the Batil camp every day - twice the established emergency threshold.
The rainy season makes it impossible to bring food in by road, and the only way to deliver aid is by air.
Some 170,000 refugees have fled to camps in South Sudan from Sudan following fighting north of the border.
"What we are seeing here in this camp in nothing short of a humanitarian catastrophe," MSF's medical co-ordinator Helen Patterson said.
Continue reading the main story
At the scene
James Copnall BBC News, Batil
The MSF clinic is full of young children crying - but often the ones not making any noise are in the most trouble.
Sadia, wearing a dirty pink dress, is lying on her side, wrapped in a blanket and a foil sheet for warmth.
She is silent, and her movements are laboured. The medical team is able, with a bit of difficulty, to put her on an IV drip, and within a few minutes she seems more lively.
Sadia is suffering from acute malnutrition, and maybe medical complications. Her mother says they walked for six weeks to get here, eating leaves to survive.
Now she is in the clinic, Sadia's chances have improved dramatically.
But many people are dying - an average of three to four young children a day, according to MSF's figures. Batil is on a flood plain, and with heavy rains expected, the fear is those numbers could get even worse.
The majority of those who have died in the camp are children under five, and MSF says that diarrhoea seems to be the biggest cause.
It adds that malnutrition is a contributing factor, calling for urgent help.
The medical charity says some 28% of children in Batil are malnourished, with 10% severely affected.
It says two people per 10,000 are dying each day - double the rate at which an emergency is declared. The camp houses some 34,000 people.
One man, Ibrahim, says his mother died after reaching Batil, in South Sudan's Upper Nile state, which stretches north between Sudan's South Kordofan and Blue Nile states, where fighting is raging between the Sudanese army and rebel groups.
Osman, another refugee, says he has already lost his nephew, and is worried that the baby boy's father will soon die too.
Refugees - many of whom walked to weeks to get to camps - say they were forced from their homes by ground and air attacks by the Sudanese military, and are being chased away because of their ethnic origin.
Officials in Khartoum deny that civilians are being targeted and blame the humanitarian situation on the rebels.
Many people in South Kordofan and Blue Nile fought with southerners against Khartoum's Islamist, Arab-dominated government for two decades. But when South Sudan gained independence in 2011, they found themselves north of the new international border.
South Sudan's government, formed by the ex-rebel movement, denies charges by Khartoum that it is backing the rebel groups on Sudanese territory.
The tension along this part of the border is one of the issues which caused Sudan and South Sudan to come to the brink of war earlier this year.