All suspects are accused of offences under Austria's law banning the spreading of Nazi ideology, with seven also accused of inciting hatred.
The raids were carried out by almost 150 officers at 11 addresses in seven of Austria's nine regions, the ministry said in a statement.
Questioning of the suspects was underway. “Mobile phones, data storage devices and other objects were seized in connection with the alleged crimes, including Nazi paraphernalia,” the statement read.
The alleged crimes took place on social media platforms such as Facebook and WhatsApp as well as in other online spaces such as chat forums on internet gaming sites.
Fourteen of the suspects possessed legal weapons while two already had already been banned from owning weapons. Some of those targeted by the raids have previous convictions for similar crimes.
Austria's 1947 law banning Nazi activity is one of the strictest in Europe.
The swoop came a day after a police operation targeted more than 60 addresses in several parts of the country that prosecutors allege were tied to radical Islamist groups.
However, prosecutors said Monday's raids were the result of an investigation stretching back more than a year, unconnected to the deadly attack by a jihadist gunman in Vienna on November 2 which left four people dead.