The ministry identified the American as 33-year-old John Michael Granfield.
USAID confirmed that Granville, 33, and Abdelrahman Abbas Rahama, 39, the driver, were shot dead.
Walter Braunohler, public diplomacy officer at the US embassy, told Reuters it was too early to speculate about motives.
"We are working closely with local authorities to investigate the incident," USAID said in a statement.
The US is the leading international donor to Sudan and has contributed nearly $2.9bn for humanitarian programmes in Sudan and eastern Chad since 2004.
The shooting came a day after George Bush, the US president, signed into a law a measure aimed at allowing states, local governments, mutual funds and pension funds to cut investment in companies doing business in Sudan, particularly its oil sectors.
Some 20 US states have initiated divestment efforts because of the conflict in Sudan's Darfur region, which has taken some 200,000 lives and displaced more than two million since rebels took up arms against the government in 2003.
"My administration will continue its efforts to bring about significant improvements in the conditions in Sudan through sanctions against the government of Sudan and high-level diplomatic engagement and by supporting the deployment of peacekeepers in Darfur," Bush said.
Bush has called the deaths in the Darfur conflict genocide, a charge the Sudanese government has rejected.
On Monday, a joint UN-African Union force took over peacekeeping operations in Sudan's western Darfur province after months of international pressure on Khartoum to allow it to deploy.