StackEdit can do that but only with Markdown documents published on Gist. By the way, you can use StackEdit to publish your document on different websites.
Update:
StackEdit can open any URL within its viewer like that:
http://benweet.github.io/stackedit/viewer.html?url=http://path/to/file.md
Update:
I'm the developer of StackEdit.
Update:
To avoid browser caching of multiple pages, use:
https://stackedit.io/viewer#!url=http://path/to/file.md
