IDPs have no basis in German law, actually, since Germany is not a a signatory to the 1949 Geneva convention on road traffic. Your national driver's licence always has to be valid, in any case.
Germany is not part of the 1949 Convention but still recognizes the IDPs. See the graphic there? I am from a country that, like Germany, is not part of the 1949 Convention, however I drove with an IDP from my home country here several times and did not have any problem. I was stopped twice by the Police, they controlled it, confirmed something over the radio (drug dealer, LOL), and let me go, once I had to pay a fine for something I did wrong.
But you do not need the IDP, your normal license is OK. The IDP only makes things easier and faster because it is translated to multiple languages.