I just ran into this same problem. And found the solution if you are hosting with Apache as your server. For instance if my settings were:

MEDIA_ROOT = '/var/www/media/geekingreen'

then I would simply need to give that folder the correct permissions recursively to make sure that any sub-folders also have the same permission. The default group for apache is www-data so to give permission to my django app I would run these commands.

cd /var/www/media
chgrp -R www-data geekingreen/
chmod -R g+w geekingreen/

The chgrp -R www-data geekingreen/ command changes the directory geekingreen and any subdirectories to have the group www-data.
The chmod -R g+w geekingreen/ command changes what permissions the group has on all of these folders that now belong to www-data, to now have the write permission. Obviously required for uploads.

Hope this can help anyone that may have had a similar problem.