The soldier, whose nationality was not released, died after he was airlifted to the mission's headquarters in the North Darfur capital of Al-Fasher.
On March 10, four Unamid troops were wounded in another ambush near Geneina in West Darfur.
Fourteen peacekeepers have been killed in the region since the joint mission took over from a struggling under-funded and under-resourced African Union mission in January 2008.
The Unamid deployment is supposed to be the world's largest peacekeeping mission but the force is currently at only 60 per cent of its mandated strength, with just 15,000 of the 26,000 planned troops and police on the ground.
Al-Bashir, who is accused of crimes against humanity during a six-year conflict in the Darfur region, is due to visit Nyala, the capital of South Darfur, on Wednesday.
According to the United Nations, 300,000 people have died and more than 2.2 million fled their homes since ethnic minority rebels rose up against the Arab-dominated Khartoum government in February 2003.
Sudan puts the death toll at 10,000 people.