Abdelrahman Mohammed Eissa, the head of Al-Waha district inNorth Darfur state, succumbed to his wounds in hospital after the attack in Kutum town, the SUNA news agency reported.
The gunmen stole the car but police and soldiers gave chase and later surrounded the suspects, SUNA said, adding the security operation was continuing.
The report did not indicate who may have carried out the attack.
Carjackings occur relatively frequently in the troubled Darfur region but such attacks against government officials are rare in Sudan.
In early July, the speaker of the legislature in Sudan’s war-torn South Kordofan state was killed in an ambush along with seven other people, official media reported. Rebels in the region denied any involvement.
The attack against Eissa in North Darfur came the day after at least eight people in South Darfur died in violence unprecedented since Arab Spring-style demonstrations began around Sudan in mid-June.
The deaths came as police and anti-regime protesters clashed in the South Darfur state capital Nyala.
Late last month, the top peacekeeper in Darfur, Ibrahim Gambari, said there had been a surge of violence in the region as he finished his tour of duty.
He said that over the preceding month, government forces staged aerial bombing raids, while rebels shot down a helicopter and staged a deadly ambush on an army convoy. Dozens have also been killed in clashes between rival tribes.
Banditry, inter-ethnic fighting and clashes between rebel groups and government forces continue in Darfur although violence is much lower than at its peak in 2003 and 2004 after non-Arab ethnic groups rose up against the Khartoum regime.