Doxygen appears to support Javadoc-style comments and can output LaTeX. LaTeX can be consumed by Pandoc, which supports Markdown output. This is somewhat roundabout, but it's the only realistic option that I can see.
Something like the following (untested)
# Generate a Doxygen configuration file, which
# should enable LaTeX output by default
doxygen -g
# Generate LaTeX documentation in the latex/ directory
doxygen
# Generate one Markdown file for each LaTeX file
find latex/ -name '*.tex' -exec mkdir -p markdown/`dirname {}` && \
pandoc -o markdown/`basename {} .pdf`.md {} \;
should get you close.
The alternative might be to take Javadoc-generated HTML and ingest that with Pandoc, outputting Markdown.