Append .wiki.git to the repository name.
That is, if your repository name was foobar:
git clone git@github.com:myusername/foobar.git would be the path to clone your repository
and
git clone git@github.com:myusername/foobar.wiki.git would be the path to clone its wiki.
Note: You must have at least one page to be able to clone the wiki repo. (via @tobiasz-cudnik)