No, since the EU decision in 2000, you do not need an International Driving Permit within the EU.
It doesn't matter whether you already have the newer EU driving licence (the plastic card) or still have the old paper driving licence. Police officers in EU countries are not entitled to ask for a translation of your driving licence.
But be careful: The driving licence of the former GDR is not recognised.
Even after Brexit, the German driving licence will be accepted in the UK.
The following article from the ADAC describes the current changes: