Zech was found guilty and given a six-month suspended sentence over the tattoo at a court in Oranienburg on Tuesday.
The tattoo featured the Auschwitz concentration camp with a slogan written across its gate, “Jedem das Seine” — “to each his own.”
The politician’s tattoo was photographed at the pool on November 21, and passed on to law enforcement.
Prosecution in the case asked that a 10-month jail sentence be handed to the politician for violating Germany’s ban on displaying Nazi symbols. Zech has previous convictions for bodily harm, according to German news outlet DPA.
Zech is currently a city council member in Barnim, a town near Berlin.