Costs of being an MS student in Germany
I've been living in Bonn for about two years now and have a monthly budget that is lower than yours (750€), but I find that this is more than enough for a relatively normal life. You should be fine as long as you live in a Studentenwerk dorm; I myself live in such a dorm and have to pay about 300€ monthly (a fee that includes both rent and utilities).

You also have to pay semester fees to your university, but that's just once a semester and it's not such a big deal (~250€ in general).

By the way, I am a scholarship holder, so I didn't mention health insurance as part of my costs; the DAAD is paying this for me. You should count on about 80€ for that as well.