"Anyone convicted under the Prohibition Act has no place in the civil service. Any form of Nazi glorification is an intolerable attack on our democratic society," Zadic wrote on Twitter.
The federal government decided to change the law, she said. "Every final conviction of civilservants automatically leads to their loss of office - the civilservants concerned must therefore leave the civil service."
The move came after an outcry about an officer who was allowed to continue working in the army although had been fined because he wore a uniform with Naziinsignia.
"It is our historical duty as the federal government to be particularly careful here and to make it clear that supporters of the anti-democratic and inhuman Nazi ideology have no place in our democratic institutions," added Zadic.
The Verbotsgesetz, or the spread of Nazism, legislation, enacted in Austria in 1947, criminalizes Nazi ideology and prohibits reviving, propagating or glorifying those views.