"There are signs of an attack with a fire bomb," the Austrian news agency APA reported Salzberg police spokesman, Hermann Rechberger, as saying.
He added that nobody was injured in the fire, which neighbours reported to the emergency services.
Fire fighters, who quickly put out the flames, said they found in one room stones and fragments from a broken bottle that could have contained a flammable substance.
Nobody was in the building when the fire began and the Turkish consul lives in another district.
Austrian police will monitor the consulate when he is there.