There is a patch for the context module to achieve exactly what your are looking for.
I've just installed it and tested it out and it works perfectly.
There is a thread on drupal.org about it here: http://drupal.org/node/904416
Scroll down to post 28 and download the patch.
To run the patch put it in the context module folder, and then run this command:
patch -p1 < 904416.28-context-query-string.patch
This is assuming you are using a linux terminal. If you want to do this in Windows or Mac then see this post: http://drupal.org/patch/apply
Once you have applied the patch then run update.php (just go to www.your_domain.com/update.php) and then flush the cache (always a good idea).
Now when you edit your context there is a new condition called Query String.
One thing to note here is that the block will only appear after the user has clicked Apply on the filter. If you want it to appear and disappear as soon as the value of the select box is changed then you will need to use Andre's solution.