Assuming you are running on an apache web server, you can setup an Alias directive to serve images from a directory outside of the normal docroot. You need access to edit the VirtualHosts config or some other ability to create aliases directives (e.g. via a control panel).
For an example of how this would work, let's say you are storing your jekyll files under a directory called "/web/jekyll". To get your images directory do the following:
Add an "_images" directory along with your basic jekyll tree. Ending up with something like:
_config.yml
_images/
_layouts/
_posts/
_site/
index.md
Update your apache config to add the Alias directive like:
Alias /images /web/jekyll/_images
Reload the apache config and run jekyll to build the site.
Since the image directory name starts with an underscore, jekyll won't push/copy it to the output _site during the build. Apache will happily serve most files from your _site directory as normal, but when it sees something like "http://jekyll/images/test.jpg", instead of looking for the file under "/web/jekyll/_site/_images/test.jpg", it'll serve it from "/web/jekyll/_images/test.jpg".
Incidentally, I like a little more separation of the source content and output content than jekyll defaults to. So, I setup my directory structure as follows:
/web/jekyll/html/
/web/jekyll/images/
/web/jekyll/source/
/web/jekyll/source/_config.yml
/web/jekyll/source/_layouts
/web/jekyll/source/_posts
/web/jekyll/source/index.md
With the following option set in _config.yml
destination: ../html
And the apache alias directive setup with:
Alias /images /web/jekyll/images
Jekyll is run in the "/web/jekyll/source" directory, but output is sent to the "/web/jekyll/html" dir. Similar to the first example, calls to "http://jekyll/images/test.jpg" are served from "/web/jekyll/images/test.jpg". This setup doesn't really make a difference from a site serving perspective. I just like the cleaner separation between the raw source files, the fully baked output files and the images which work via the alias.