Two security sources were said to have confirmed the death and indicated that an investigation was ongoing.
The name of the diplomat is yet to be given.
NAN reports that officials from the Nigerian embassy in Khartoum were not immediately available to comment.
According to Reuters, a television station, al-Arabiya, identified the diplomat as the consul general and described his death as an “assassination”.
Though intermittent violence is common in Sudan’s warring southern and western regions, violence in the capital is rare.
Sudan’s President Omar al-Bashir has in recent months shaken up the security establishment, replacing the heads of the army and intelligence service in February.