I just wrote out a detailed response, but somehow, I hit the wrong button, and it got lost. So, here's my best attempt at re-creating it:
1. Regardless of how you found out about it, you are now aware of some type of problem with your employees.
2. As the supervisor, you are responsible for dealing with work-related problems and issues with your employees.
3. If you don't address it now, while it's likely a small problem, as you mentioned, if it blows up later, the fingers will point at you....especially if this ends up involving some kind of harassment, EEO or similar complaint.
4. You HR director and your direct supervisor should be consulted---to make them aware and to seek direction on the next step. This protects you, as well, if it turns into something bigger.
5. The employee who posted on FB, at the very least, should be made aware that social media is not the proper place to air work-related problems, and should be reminded of the proper chain of command for work-related complaints.
6. Your company should review its policy with respect to social media and the workplace (or devise one if it is lacking) and educate staff.
(My .02 here: Social media is a relatively new phenomenon, but it's so pervasive and such a part of so many people's lives, especially the younger generation, that some don't realize there are limits when it comes to the interface between their professional lives and their "free speech" on social media. Anyone who thinks social media is private and separate from work is out of touch with the reality of the work/professional world).
7. Document what you did to address this problem.
Hope this helps. Good luck!
J. F.