The image of the uniform, showing three swastikas and posted in an Instagram story, was captioned: "Also #fashion is an aspect. To this day there are military-style elements of haute couture."
At a government press conference in Berlin, defense spokesman Christian Thiels said this was an "unacceptable mistake" for which the ministry "apologizes."
Thiels explained he had spoken with, and reprimanded, the employee who posted the image.
The spokesman also admitted that this incident damaged the reputation of the German military (Bundeswehr) and said the post had caused "considerable irritation."
It was not clear from Thiel's explanation how the post came about.
According to the German defense ministry, the editorial team at the German armed forces had taken a series of photos in the military history museum in Dresden. One of the images was of the uniform, which is a prop from the 2008 Nazi thriller "Valkyrie."