The attack occurred at around 1300 GMT some 90 kilometres (56 miles) northeast of the South Darfur state capital Nyala, UNAMID said.
It did not give the nationality of the victims but Nigerian troops operate in that area.
“Four peacekeepers were initially injured. One died seeking medical treatment,” UNAMID spokesman Christopher Cycmanick told AFP.
He said it was not immediately clear how seriously injured the others were.
UNAMID said its peacekeepers returned fire.
“We don’t know if there were casualties on the other side,” Cycmanick said.
This is the second fatal shooting of a UNAMID peacekeeper this year.
In January an ambush near El-Daein, in southeastern Darfur, killed a Nigerian UNAMID member and wounded three others, prompting the UN Security Council to call for “an end to impunity for those who attack peacekeepers.”
Thirty-six blue helmets have been killed in Darfur since UNAMID was deployed in 2007 to protect civilians.
Rebel groups drawn from Darfur’s non-Arab tribes rose up against the Arab-dominated Khartoum government in 2003. In response, the government unleashed state-backed Janjaweed militia in a conflict that shocked the world and led to allegations of genocide.
Since then, much of the violence in the vast western region has degenerated into banditry.
Last Friday two UNAMID police officers were shot and wounded near El-Daein.