The wall of the building in Erlachstrasse was defaced sometime during Saturday night, police said. A second building in Bahnhofstrasse was also daubed with similar graffiti.
Police are looking for the perpetrators, who could be charged with xenophobia and violating the prohibition law which outlaws any revival of Nazism.
Anyone who was in the area on Saturday night and noticed anything unusual or suspicious has been asked to get in touch with the police in Hohenems, by calling 059 133 80 1133 or 059 133 801 133.
A police spokesman said there would not be an increased police presence around the refugee centre, but that routine patrols will be checking on it regularly.