The killings came as fears are growing of attacks on foreign aid groups in the region.
The workers were assaulted on Saturday evening on the road to the settlement of Khor Abeche, north east of Nyala, the south Darfur capital, a spokesman for the United Nations Hybrid Operation in Darfur (UNAMID) confirmed.
Frederic Mar, from Aide Médicale Internationale, said the bus the aid workers were on was stopped by the armed group, who opened fire when the passengers panicked, killing two members of staff and injuring four civilians.
Tension has increased in Darfur as the International Criminal Court (ICC) considers whether to issue an arrest warrant for Omar al-Bashir, the Sudanese president, for alleged war crimes.
ICC judges are expected to rule on a decision within weeks.