"This morning, gunmen in South Darfur opened fire at a UN patrol, killing Jordanian Major Talal Rjub and a Senegalese peacekeeper," the statement said.
"The United Nations peacekeeping force has informed us of the attack and said it was investigating it," the statement added without elaborating.
More than 12 peacekeepers from the African Union-UN peacekeeping mission in Darfur (UNAMID) have been killed in the region in the past five months.
In January, two Jordanian peacekeepers were freed after more than four months in captivity in Darfur. The men went missing in August 2013 as they shopped for supplies.
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A new surge in fighting this year has been blamed on rivalry between Arab tribes in the western region. Hundreds have died in clashes between different tribes and militias.
The UN-African Union mission has more than 25,000 troops and police in Darfur.
More than 3,000 members of Jordan's armed forces serve with international peacekeepers around the world.
"Jordan has the second largest peacekeeping force working under UNAMID in Darfur," a security official told AFP without giving precise figures.