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."
Thiels said he had no explanation as to why the employee posted the image.
Though this was "an extremely annoying case of thoughtlessness," the employee has no political background motivation to post the image, Thiels said.
Tobias Linder, a member of Germany's parliament representing the Green Party, said in a statement posted to Twitter Wednesday that he was "outraged" by the post, and demanded an explanation as to how it had made it on to the official account, which has more than 300,000 followers.
The German military apologized for the incident on Wednesday in a series of tweets, stating that "extremism of any kind is an absolute no-go" in the Bundeswehr.
"The intention was to show a photo story about the centuries-old influence of uniforms on fashion. Unfortunately we have published this mistakenly with the multiplicity of the photos provided by us. Naturally, all this should not have happened," the official Bundeswehr account posted.
"We are now investigating what went wrong and how we can prevent this in the future."