Government forces have been battling rebels for the past two years, although a peace deal was signed in August.
Niger is a close second, with 47% unable to attend school, followed by Sudan (41%) and Afghanistan (40%).
Worldwide, some 24 million children of more than 109 million living in nations at war are not in school, Unicef said.
Even before the conflict began, 1.4 million children were already missing class in South Sudan, Unicef said.
Since the war broke out, more than 800 schools have been demolished and more than 400,000 children had to abandon their classrooms, the agency said.
Despite the peace agreement, violence persists in some areas.
Only one in 10 South Sudanese students who enter school finish primary education amid a shortage of facilities and trained teachers, said Phuong T Nguyen, Unicef's chief of education for South Sudan.
"There is a very, very low budget from the government to the education sector," she said. "It is not holding steady and we see a decline."
Enrolment went up from under 30% after South Sudan became independent in 2011, but the war and a lack of school buildings and qualified teachers have slowed the growth, according to a South Sudanese official, the AP news agency reports.
More than half of children in South Sudan are not in school, the highest proportion in any country, UN children's agency Unicef has said.