Brandenburg state police say they are working on the assumption that the fire was started deliberately. Nobody was injured.
Far-right protesters had repeatedly demonstrated against the arrival of asylum-seekers in Nauen this year.
Germany has seen a surge in refugees coming to the country this year, with officials predicting the number could reach 800,000 by the end of 2015.
While most Germans have been welcoming to the refugees, a minority has vocally opposed them. Chancellor Angela Merkel yesterday condemned neo-Nazi riots outside a home for asylum seekers in Heidenau, south of Dresden, over the weekend.