Internet dating does connect one with the most interesting people, doesn't it? While multicultural experiences are enriching, I can hardly blame you for not wishing to carry on a meaningful relationship with a zombie.
The normal rule of thumb in this situation would be to simply inform a gentleman that, while you've enjoyed getting to know him, you don't feel like there is a lasting future to the relationship. A polite, "thank you for being such a charming dinner companion" makes this kind of an awkward conversation go much more smoothly.
However, since the gentleman in question is a zombie, there is really only one course of action that is appropriate in polite society.
Cut off his head.
A gunshot to the brain is also an option, but I find beheading much cleaner and more precise. Leave too much of the brain still functional and you can't tell what kind of half headless monster might show up at your door looking to take you out for ice cream. Beheading leaves you with no if's, and's or but's. Or heads.
Just be sure to carry out the procedure in a place that makes disposal of the body convenient. Garbage dumps, Wal Marts (known to be home to the latest species of carrion eating bunny rabbits) and freeway's are recommended.
Good luck in your search for love Miss Famine.
Emily Post Apocalypse