As a homeowner, you are required to pay a quarterly land tax which is dependent on the value dictated by your local Finanzamt. The property tax is generally no more than 150 euro per quarter, based on 41 million German households.
The tax rates that are quoted as a percentage that you may see in news items sound scary, when you apply them to the prices of current houses. In practice however, the rates are applied to extraordinarily low property values--think two hundred year old values. This is why the actual tax is relatively low.
Anything you may ever want to know about this topic you can find here: https://de.wikipedia.org/wiki/Grundsteuer\_(Deutschland)