An air base detected the target around 10:45 pm (1945 GMT) yesterday flying at low altitude over Omdurman's Wadi Sayidna military area, checked there were no civilian planes nearby and shot it down, military spokesman Colonel Al-Sawarmy Khaled Saad said in a statement.
After it was hit, it disintegrated and its debris fell to earth in several residential areas of Omdurman, Saad said.
Saad described the downed aircraft as a "photographic surveillance target," but said it was still unknown where it came from and did not specify if it was a drone.
Investigations were ongoing, Saad said, stressing the "stability of the situation" in the capital today.
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In an earlier statement, Saad had denied rumours of "an attempted coup, military clashes or a foreign attack" that circulated on Sudanese social media after the incident.
Witnesses in Omdurman said they heard loud explosions from outside the city late yesterday. The area is home to several military installations.
A resident of the city's Wad al-Bakhit neighbourhood told AFP they had heard several loud blasts.