The attack took place in the Hammadeh area 80 kilometres north of the state capital Nyala, the statement carried by official new agency SUNA said Wednesday.
"We have formed a commission of inquiry into the killing of the citizens in the Hammadeh area," state governor Adam Jar al-Nabi told SUNA.
One of those wounded who talked to SUNA from the hospital in Nyala said the group had been visiting family in Hammadeh and were returning on Tuesday when the attack took place.
Two of the casualties died on Wednesday morning from their wounds, he added.
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The report did not say how many gunmen had attacked the vehicle and gave no indication of their identity.
The troubled western region of Darfur has been wracked by lawlessness since 2003, when ethnic insurgents rebelled against the mostly Arab government in Khartoum, complaining of their marginalisation.
The conflict has claimed 3,00,000 lives and displaced two million people, according to the UN, and President Omar al-Bashir and his defence minister are wanted by the International Criminal Court for alleged war crimes in the region.