Many of the 26 soldiers belong to a logistics unit in Neustadt am Ruebenberge in northern Germany, the ministry said in a report to parliament dated Friday and first reported by public ARD television.
Civilian and military prosecutors started investigations immediately after the accusations became known in October, it added. So far, three of the soldiers have been banned from wearing a uniform and working for the military, the document said, without elaborating.
The case is the latest in a series of far-right scandals to surface in the German military.
In June, Defence Minister Annegret Kramp-Karrenbauer disbanded a company of the army's elite KSK special forces after recurring incidents involving far-right extremism.
"The deeper you dig into the forces, the more right-wing activities you find," Alexander Neu, a lawmaker with the opposition far-left Linke, told Reuters.
"This shows that the fondly nourished hypothesis that we are talking of isolated cases is just a fairy tale."