Upvote:3
I would also recommend HouseTrip.com. We used it to find apartments in Budapest, Prague and Vienna and had a great experience overall! I was impressed by how flexible the search feature was (i.e., we were able to search for centrally located apartments that can sleep 6 people and that include WiFi and laundry).
Upvote:4
If you are searching for an unfurnished apartment, this is the most popular site in Germany:
http://www.immobilienscout24.de
Otherwise, you can check Craigslist Munich for apartment listings, almost all of which are furnished. Alternately run a simple search on Google for "Furnished apartments Munich" and you will see lots of different companies providing basically the same service.
Edit: I misread the original question, the OP is only staying for a very short amount of time. My advice is best suited for people staying over a year.
Upvote:7
If you don't speak German, Airbnb is your best bet. For the period you mention, they feature some 150 entire apartments that are suitable for 2 persons.