You can add this to your htaccess to ignore rewriting favicon.ico and anything with the extensions in the parens
RewriteCond %{REQUEST_URI} !\.(gif|jpe?g|png|ico)$ [NC]
So your htaccess would look like
RewriteEngine on
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_URI} !\.(gif|jpe?g|png|ico)$ [NC]
RewriteRule ^(.*)$ /index.php