"We are now unfortunately certain that two soldiers in service of our country have lost their lives. Their mission was a contribution to our security," the minister told reporters at a briefing.
German President Frank-Walter Steinmeier and Chancellor Angela Merkel have both extended their condolences to those affected.
Joachim Ruehle, deputy spokesman for the inspector general of the German armed forces, said the cause of the crash was still unclear but there was no indication that the Tiger-type combat helicopter had been shot down.
"The initial report of the crash came from a second, following helicopter. There was no distress signal from the affected crew. The crashed helicopter burned out… At this time, nothing points to outside interference," he said.
A spokesman for the UN secretary general said earlier that the search for the crashed aircraft had been complicated by fighting on the ground, which it was monitoring.