In recent years, digitization of cultural heritage objects, for the purpose of creating virtual museums, is becoming increasingly popular. Moreover, cultural institutions use modern digitization methods to create three-dimensional (3D) models of objects of historical significance to form digital libraries and archives. This research aims to suggest a method for protecting these 3D models from abuse while making them available on the Internet. The proposed method was applied to a sculpture, an object of cultural heritage. It is based on the digitization of the sculpture altered by adding local clay details proposed by the sculptor and on sharing on the Internet a 3D model obtained by digitizing the sculpture with a built-in error. The clay details embedded in the sculpture are asymmetrical and discreet to be unnoticeable to an average observer. The original sculpture was also digitized and its 3D model created. The obtained 3D models were compared and the geometry deviation was measured to determine that the embedded error was invisible to an average observer and that the watermark can be extracted. The proposed method simultaneously protects the digitized image of the artwork while preserving its visual experience. Other methods cannot guarantee this.