War broke out in Sudan, one of the world's poorest countries, in April last year, leading to a humanitarian collapse.
The conflict has already displaced more than 9 million people, according to U.N. figures.
The Zamzam camp in North Darfur is one of the largest camps for displaced people in the country.
"What we are seeing in Zamzam camp is an absolutely catastrophic situation. We estimate that at least one child is dying every two hours in the camp," Claire Nicolet, head of MSF's emergency response in Sudan, said in a statement.
That amounted to around 13 child fatalities a day, she added.
"Those with severe malnutrition who have not yet died are at high risk of dying within three to six weeks if they do not get treatment. Their condition is treatable if they can get to a health facility. But many cannot," Nicolet said.
Nearly a quarter of the children screened were suffering from acute malnutrition, and nearly 40% of children aged between six months and two years were malnourished, exceeding "all emergency thresholds," said the NGO.
Similarly, the number of deaths in the camp, which is home to an estimated 300,000 to 500,000 people, was also "cause for extreme alarm," with a crude mortality rate of 2.5 per 10,000 people per day, more than double the emergency threshold, said the French charity.
MSF said it was the only operational health provider in the Zamzam camp.
Nicolet said people "have been almost completely abandoned."
"There have been no food distributions from the World Food Program (WFP) since May," she added. "People are going hungry — and children are dying as a result."
There is also no clean water supply, with people drinking either from the swamps or from the river, the charity said.
MSF said it would "rapidly increase" its response in the camp, but added that "a far greater response" was needed.
Separately, U.N. experts said around 25 million people, including 14 million children, were in dire need of humanitarian assistance in Sudan.
The conflict between Sudan's army chief Abdel Fattah al-Burhan and his former deputy, Mohamed Hamdan Daglo, commander of the paramilitary Rapid Support Forces (RSF), erupted last April.
Diplomatic efforts to end the violence continue after numerous ceasefires have been broken.
The war has already killed thousands, including between 10,000 and 15,000 in a single city in the western Darfur region, according to U.N. experts.
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