"At the moment, we assume there were seven seriously injured but at present, none of them are in danger of dying," Christian Dienst told a regular press conference.
The incident appeared to be an accident rather than a deliberate attack, an army spokesman said. The driver of the Mercedes apparently failed to see the troops in the dawn light.
According to rolling news channel N24, the wounded were soldiers at a military base in Bad Salzungen, central Germany, who were preparing to take part in an exercise. The base is home to around 1,000 soldiers.
Around 10 ambulances and three helicopters were at the scene, N24 reported.