**Quick and dirty way**: create a polygon for the complement of the region to be shown (by subtracting the region from a large rectangle, for instance).  Draw this polygon over the raster.

**Better**: the states should be polygons.  Convert the state layer to a raster.  Use that as a mask to clip the image.  For a tutorial, see [Better Raster Clipping Options in ArcGIS][1].

BTW, the image cannot be "displayed in shapefiles" because shapefiles (a) do not store images and (b) do not store graphical information.  They store only the coordinates for representing vector features.


  [1]: http://blogs.esri.com/Dev/blogs/geodatabase/archive/2009/05/06/Better-Raster-Clipping-options-in-ArcGIS.aspx