Have the server interpret www.example.com/directory as a directory rather than a Drupal path
So, your drupal site lives at webroot, and your wiki lives at webroot/wiki? First thing i would suggest is to put your wiki outside your drupal root and creating a separate virtual host. You're asking for trouble with your current setup.

The .htaccess file that ships with Drupal should properly be treating webroot/wiki as a directory, if it exists. See https://stackoverflow.com/questions/15879029/dont-understand-rewritecond-request-filename-f-and-d

If it just won't work for you, update Drupal's .htaccess to explicitly add your wiki path:

RewriteCond %{REQUEST_URI} ^/wiki


Put this right before:

RewriteRule ^(.*)$ index.php?q=$1 [L,QSA]


Your rewrite section will look like this (comments elided):

RewriteEngine on
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_URI} !=/favicon.ico
RewriteCond %{REQUEST_URI} ^/wiki
RewriteRule ^(.*)$ index.php?q=$1 [L,QSA]