"He was ambushed on Saturday by men who wanted his Thuraya satellite telephone," Simmons said.
"They came to his home on Monday evening to take the phone, but it wasn't there. The armed men then opened fire on him."
Aid workers have experienced increased hostility in Darfur after the International Criminal Court (ICC), based in the Hague, issued an arrest warrant for Sudan's president on March 4, for alledged war crimes and crimes against humanity in the region.
Omar al-Bashir, Sudan's president, reacted by expelling 13 international aid
agencies from Darfur earlier this month.
Increased violence
A peacekeeper with the joint UN-African Union force (Unamid) in Sudan's western Darfur region was shot dead on March 17 in an ambush by eight unidentified gunmen on his way back from a patrol.
Three foreign aid workers were kidnapped on March 12 in Darfur and released four days later.
And on March 10, four Unamid troops were wounded in another ambush near Geneina in West Darfur.
Despite the international court order for his arrest, al-Bashir is expected to visit Egypt on Wednesday, Egyptian officials said anonymously as the visit has not yet been officially announced.
Al-Bashir would meet Husni Mubarak, the Egyptian president, to review the ramifications of the ICC arrest warrant for him, the sources said.
It would be the president's second trip abroad since the arrest order was
issued. He briefly visited the African nation of Eritrea on Monday.
Egypt belongs to the 22-nation Arab League which has said its members will
not arrest al-Bashir.
Arab summit
Sheikh Hamad bin Jassem al-Thani, the prime minister of Qatar, travelled to Sudan on Tuesday in an attempt to convince al-Bashir to attend this weekend's Arab summit in the Qatari capital, Doha, where they will focus on the situation in Darfur.
The Qatari prime minster said during his visit that Doha was put under pressure by several parties to abstain from receiving al-Bashir.
"Doha would not acquiesce to such pressure while al-Bashir is absolutely free to take the appropriate decision about attending the Arab summit", the Qatari prime minister said.
Earlier this week, Islamic scholars in Sudan advised al-Bashir not to travel to Qatar, saying the risks of him being arrested were too high.
Before the authority issued its statement, Mahjoub Fadul, the Sudanese presidential spokesman, told the Reuters news agency security arrangements had been put in place in case al-Bashir did make the journey.
Qatar is not a member of the ICC and would have no legal obligation to arrest al-Bashir if he entered its territory.
Amr Mussa, the Arab League secretary-general, said last week that the 22-nation group would not act on the arrest warrant.