The killing came as officials announced an agreement on aid access to South Kordofan and Blue Nile, where the UN has described a worsening humanitarian crisis but has been severely restricted in its movement.
"Our driver was killed yesterday in an armed attack in an area some 80 kilometres (50 miles) north of Kadugli," WFP spokeswoman Amor Almagro told AFP.
Jamal Al Fadil Farag Allah, married with five children, is the first WFP employee to be killed in Sudan, she said.
"He was driving fellow staff member Saad Yousif when their vehicle was attacked by two unknown assailants," Almagro said.
They were travelling on a main road in a marked UN vehicle on official business, she added.
Yousif was wounded but survived and was to be airlifted to Khartoum later on Sunday.
More than 200,000 refugees have fled a worsening humanitarian situation in South Kordofan and nearby Blue Nile states since fighting between government and rebel forces from the Sudan People's Liberation Movement-North (SPLM-N) began in June last year, the United Nations says.
Ethnic minority insurgents of the SPLM-N fought alongside southern rebels during Sudan's 22-year civil war, which ended in a 2005 peace deal and South Sudan's independence in July last year.
There are no figures for how many people have died since the war in South Kordofan and Blue Nile began.
The government of Sudan has cited security concerns in placing tight restrictions on the operations of foreign relief agencies in the warzone.
After African Union-led talks in Ethiopia, AU mediator Thabo Mbeki on Saturday announced an agreement between Sudan, the United Nations, the AU and the Arab League to allow for humanitarian access in South Kordofan and Blue Nile.
Sudan has agreed to allow an independent assessment of the humanitarian needs, as well as internationally-monitored delivery of aid throughout the war zone, a foreign analyst said.
However, a ceasefire will be required to implement the measures, he added.
Progress on aid is unlikely until the political side is addressed as well, "including a possible ceasefire", a humanitarian source said.
The European Union's foreign policy chief Catherine Ashton said she was encouraged that Sudan had reportedly agreed on "modalities" for delivering aid to all civilians affected by the conflict.
She urged immediate implementation of the deal which "needs to be accompanied by a cessation of hostilities and political negotiations between the government of Sudan and the Sudan People's Liberation Movement-North."
The WFP worker's death came two days after armed men in another part of the country spent about 12 hours looting and ransacking a WFP compound, Almagro said.
The incident began at about mid-day Thursday and continued until early Friday at the compound in Kutum town, North Darfur, she said.
"Our office and guest house were looted," with furniture, fuel, computers and other items stolen, Almagro said. WFP staff hid during the incident and were unhurt.
"Since the security situation remains tense and unpredictable we have decided to suspend our operation until the situation calms down," she said.
WFP recently completed a food distribution to about 70,000 people in the area, meaning the suspension will not have an immediate impact on their food supply.
The attack against the WFP office came a day after a district chief died from gunshot wounds suffered in an ambush of his car in Kutum, raising tensions.
A Briton who worked for WFP in Nyala, South Darfur, was kidnapped earlier this year and spent nearly three months in custody before his release in May.
Banditry, inter-ethnic fighting and clashes between rebel groups and government forces continue in Darfur, in Sudan's far-west, although violence is much lower than at its peak in 2003 and 2004 after non-Arab ethnic groups rose up against the Khartoum regime.