The incident occurred on Monday in the region where, according to the UN, fighting between two Arab tribes this month killed 190 people.
An "unknown armed group" attacked a patrol of the African Union-UN Mission in Darfur (UNAMID) about 36 kilometres (22 miles) northeast of the East Darfur state capital Ed Daein, said Rania Abdulrahman, a UNAMID media officer.
"During the firefight three peacekeepers sustained gunshot wounds," she told AFP.
On August 12 a UNAMID police patrol was ambushed in Ed Daein but there were no injuries, UNAMID said earlier.
The region surrounding the town was the scene of fighting between the Rezeigat and Maaliya tribes this month.
Last Friday the UN's Office for the Coordination of Humanitarian Affairs reported that aid groups "remain deeply concerned about the insecurity in East Darfur".
UNAMID says inter-ethnic fighting has been largely responsible for an upsurge of violence in Sudan's far-west this year.
Hundreds of people have died in the tribal battles, largely between Arab groups, and hundreds of thousands of others have been displaced.
Thirteen peacekeepers have been killed in hostile action in Darfur since last October.
One of those deaths came in April when "armed men in military uniforms" attacked a UNAMID base in the Muhagiriya area, UN Secretary General Ban Ki-moon reported in July.
Muhagiriya is about 100 kilometres northwest of Monday's attack.
Seven UNAMID troops were killed last month during an ambush north of Nyala, South Darfur's capital. It was the worst-ever attack in the mission's five-year history.
UN sources say they are unaware of anyone having been held accountable in Sudan for killing a peacekeeper, despite repeated UN calls for perpetrators to be brought to justice.
Non-Arabs in Darfur rose up 10 years ago against what they saw as the domination of Sudan's power and wealth by Arab elites.
In response, government-backed Janjaweed militias shocked the world with atrocities against them.
Although the rebellion continues, analysts say Sudan's crisis-hit regime now has less money for its militias, who are acting outside government control and have been a major contributor to violence in the region this year.