Fifty other detainees were wounded in the attack on the main prison in Obeid, the capital city of North Kordofan, Information Minister Khalid Aleiser said in a statement.
Aleiser, who is also the spokesman of the military-allied government, accused the Rapid Support Forces for the attack, which came as the militia escalates drone strikes on the military-held areas across the country.
Sudan plunged into civil war on April 15, 2023 when simmering tensions between the military and the RSF exploded into open warfare in the capital Khartoum and other parts of the country.
Obeid is 363km south of Khartoum.
There was no immediate comment from the RSF which earlier this month launched multi-day drone attack on Port Sudan, the Red Sea city serving as an interim seat for the Sudanese government.
The strikes hit the city's airports, maritime port and other facilities including fuel storages.
The military earlier struck Nyala airport in South Darfur, where the RSF receives foreign military assistance including drones.
Local media say dozens of RSF officers were killed in last week's strike.
In the western region of Darfur, an artillery attack by the RSF on Friday on a camp for displaced people killed at least 14, according to the Emergency Room, an activist group tracking the war.
The dead included two parents, their eight children and the children's grandmother, the group said.
The RSF has launched nearly daily attacks on the camp and the nearby city of el-Fasher, the provincial capital of North Darfur, which the paramilitaries have attempted to seize for more than a year.
Last month the RSF rampaged through Sudan's largest camp for displaced, Zamzam, killing more than 400 people.
The militia took control of the camp, pushing its population to flee.
The war has killed at least 24,000 people although the number is likely far higher.
It has driven about 13 million people from their homes, including four million who crossed into neighbouring countries.
Parts of the country have been pushed into famine.
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