Killed was Jimmy Lemi Milla, minister of Cooperatives and Rural Development, as well as his bodyguard, the Sudan Tribune reported.
Police said Milla was shot after he entered his office in Juba, the capital of Southern Sudan, which recently voted to split from the government based in northern Sudan.
The driver has been detained, Philip Auger, a spokesman for the Sudan's People's Liberation Army, told CNN.
"The gun was taken from him and he was arrested," Auger said.
Officials have not given a reason for the shootings.