German military intelligence had investigated Maximilian T.in September 2015 after a fellow soldier reported that he had tried to recruit him to attack non-Germans, according to sources familiar with the matter.
Prosecutors said he was suspected of acting on "right-wing extremist conviction".
German Defence Minister Ursula von der Leyen on Wednesday said she would respond to the discovery of far right sympathizers in the German army with reforms, including revising one of the force's post-Nazi era founding principles.
Maximilian T is believed to be an accomplice of Franco A, a 28-year-old man who was arrested on 26 April after police discovered he had registered as a Syrian refugee - even though he spoke no Arabic - and planned to carry out xenophobic attacks.
The move follows the arrest of two officers suspected of plotting an attack disguised as Syrian refugees.
The pair, along with 24-year-old student Mathias F, had hoped the murder would "be seen by the population as a radical Islamist terrorist act committed by a recognised refugee", said the prosecution.
The Bundeswehr is now conducting searches of army barracks across the country in search of Nazi-era memorabilia as part of the probe into far-right sympathizers.
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The initial warm reaction the asylum seekers from Syria, Iraq, and Afghanistan received upon arrival in Germany has soured, with several high-profile incidents leading to an anti-Muslim backlash, rising nationalism, and hate crimes.
The arrest was made in the southwestern town of Kehl.
The arrested members of the German armed forces are suspected of planning a "serious attack on national security", federal prosecutors in Karlsruhe confirmed on Tuesday.
Der Spiegel magazine said T, whose last name wasn't given in line with privacy laws, was a Bundeswehr soldier stationed at the same Franco-German brigade in Illkirch, just across the border from Kehl, with Lt Franco A, who was detained last month. Franco A. and Mathias F. were named by police in the plot to assassinate former German President Joachim Gauck, Justice Minister Heiko Maas and others.
German Defence Minister Ursula von der Leyen gives a statement to the media prior she faces the defence commission of the lower house of parliament Bundestag in Berlin, Germany May 10, 2017.
Von der Leyen has apologised for her sweeping criticism of "weak leadership" in the military, saying she regretted not balancing her remarks with appreciation for the work done by the majority of the armed forces.
The soldier had previously been detained in late January by Austrian authorities on suspicion of having hidden an illegal gun in a bathroom at Vienna's main airport, Schwechat.