Had a very good vegetarian dinner at Pardi last week; it is a Turkish restaurant with quite a few vegetarian options: www.pardi-restaurant.de Easy access from the city center via U-bahn; closest stop is Rotkreuzplatz.. They have daily specials in addition to their regular menu.
Dinner with appetizer, main course, drinks and shared dessert (awesome baklava) ran 20-25 euros pp. They're also open for breakfast and lunch from 9 a.m.
Menu is in german, but waitstaff speaks some English and is very helpful.
As tmso mentioned, Germany has a lot of vegetarians, and at least a few of them live in Munich (population > 1 350 000 in 2007)
Prinz Myschkin and Zerwirk are 2 exclusively vegetarian restaurants in Munich.
earlier threads that might help you:
Here is a list of veggie-friendly establishments in Munich:
You certainly won't starve. The food in Bavaria is quite good, and unlike its western and southern neighbors, Germany has a lot of vegetarians, so you'll have something to eat.
Fridays in particular should be easy almost anywhere. Non-meat main dishes are common on Fridays ... they're sometimes fish, but often Spätzle or Maultaschen or if you go during asparagus season, based around asparagus and eggs.
Not being a vegetarian myself, I don't have too many specifics to offer, but I can recommend Vegelangelo on the Thomas-Wimmer-Ring.