The health ministry blamed the deaths on human error. One syringe was used for all the children, and the vaccine was not stored properly.
Measles is yet another challenge facing the desperately poor country that already has been devastated by more than three years of civil war and a recently declared famine, as well as a cholera outbreak.
The government said all of the children who died were under the age of 5. It is setting up a commission to determine who is responsible and whether victims' families will be compensated.
The children died in the town of Kapoeta in early May, and other children have become gravely ill after vaccination campaign.
Abdulmumini Usman, the South Sudan country director for the World Health Organization, told The Associated Press earlier this week that even after the organisation became aware of the deaths, the measles campaign continued across the country except in Kapoeta.
"This campaign is lifesaving," Usman said.
WHO provides some training to South Sudan's health officials and the UN children's agency provides the vaccines to the government. It was not immediately clear whether any UN officials were present at the time of the botched vaccinations.
The civil war has killed tens of thousands and sent more than 1.8 million people fleeing the country, creating the world's fastest-growing refugee crisis.
In 2016, South Sudan had at least 2,294 measles cases and 28 people died, according to UN data.
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