The radio said the deputy minister, Col. Ibrahim Shamsul-Din, and the others had been touring a southern military area and were headed back to Khartoum at the time of the crash.
Shamsul-Din had backed the coup in which Sudanese President Omar el-Bashir took power in 1989. The military remains the main power broker in Sudan, not least because the country has been embroiled in civil war for 17 years.
The dead included another colonel, nine lieutenant generals and three brigadier generals.
The accident took place in Adaril, in an oil-rich area 470 miles south of Khartoum, the radio said. The cause of the early morning crash was not immediately announced.
The blow to Sudan's military hierarchy comes at a time the country was believed to be using its newfound oil wealth to take the upper hand against southern rebels.
Nearly 2 million people have died in the conflict between Sudan's Islamic government in the north and rebels fighting for increased autonomy in the predominantly Christian and animist south.
By Mohamed Osman
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