Great question! I am not aware of any such place but will keep my eyes open. I hope to visit Berlin sooner than later & would greatly appreciate it if you share what you find out and tell us how your visit goes.
Personally I would just find a hostel in an area you like and then either go out eat or bring food back to prepare at the hostel. Another option is http://www.couchsurfing.org - lots of vegan CouchSurfers in Berlin! :)