I don’t think it’s possible to make a usable Javadoc with MarkDown. The best solution is probably to commit the Javadoc you generated on the gh-pages branch (or in the docs/ directory depending on the settings of your GitHub project). It will be available at :
http://username.github.io/projectname
Here is an example from one of my projects:
http://ebourg.github.io/jsign/apidocs/
I used to do this but nowadays I just rely on javadoc.io to host the Javadoc:
https://javadoc.io/doc/net.jsign/jsign/
The documentation is picked automatically from Maven Central, this saves the extra step of commiting the files into the Git repository when preparing a new release.