You may drive in Germany with your valid full Indian licence for the period of up to six months upon entering Germany if you intend to stay there only temporarily.
You are not obliged to obtain an international drivers licence for that period of time. However, it could still prove useful as you may be asked to provide a German translation of your Indian licence by the German police or car rental staff.
Once you have stayed in Germany longer than 6 months, you are required to apply for a German drivers licence. Indian licences are not simply exchanged for German ones, you will be asked to pass a full theoretical and practical driving test.