The incident happened near the airport outside Ed Damazin, the capital of Blue Nile state, said army spokesperson Sawarmi Khaled Saad.
“A military helicopter on a training flight crashed into an electricity tower,” he said.
Rebels claimed to have shot down the aircraft, although the Damazin area is government-controlled.
Insurgents of the Sudan People’s Liberation Movement-North (SPLM-N) in Blue Nile and South Kordofan have been fighting for two years.
Last Friday the Sudan Revolutionary Front, a rebel coalition to which SPLM-N belongs, said it shot down a military helicopter in South Kordofan.
A witness there reported seeing smoke trailing from the aircraft above the town of Abu Kershola.
The military relies heavily on air power in its campaign against the SPLM-N, as well as in battle against rebels from Darfur, in Sudan’s far west.
The air force fleet of Russian-made planes and helicopters has suffered a number of losses in recent years, with the military frequently blaming technical problems.