Suspicions arose following a monthslong intelligence operation by the Military Counterintelligence Service (MAD). The officer, who has served several tours of duty in Afghanistan, was being covertly investigated by the service after an informant tipped them off to the man's activities.
MAD recommended that the officer be removed from the Special Forces Command immediately and barred from serving in the Bundeswehr. He is due to leave his post this week.
Two other soldiers in the Special Forces Command are also on the radar of Bundeswehr investigators for right-wing extremist activities.
The two men are accused of flashing the Nazi-era Hitler salute at a private party that was hosted by the suspected KSK officer.
Vigilante groups cause alarm
Making the gesture and using other Nazi symbols is illegal in Germany.
One of the soldiers was suspended from duty a few weeks ago and is no longer allowed to wear a uniform, Bild am Sonntag reported. The other soldier is still under investigation.
Military has 'responsibility' to remove radicals
Defense Minister Annegret Kramp-Karrenbauer said the military is taking the cases "very, very seriously" and vowed tough action against extremists found in its ranks.
"Anyone in the Bundeswehr who appears to be a radical has no place in the Bundeswehr," Kramp-Karrenbauer said Sunday during a visit to Kosovo.
She added that the Special Forces Command in particular has a "special responsibility to counter any tendency toward radicalism."
KSK is particularly responsible for rescuing people who have been kidnapped, taken hostage or are facing terrorist threats abroad.
Christof Gramm, the head of MAD, recently reported that they are currently investigating 20 soldiers in the elite unit over suspected links to right-wing extremists.
Concerns over right-wing extremists or neo-Nazis within the ranks of the Bundeswehr heightened after an officer was accused in April 2017 of planning a far-right terror attack that he hoped would be mistaken for Islamist extremism.