I can appreciate it. But FaceBook isn't considered the same as taking out an ad in the paper or putting up a billboard. He's allowed to say whatever he wants, until it becomes hate speech, criminal harassment, or a threat. Your girlfriend should be upset more with whoever told him.
Regardless, your girlfriend shared her medical information with people who blabbed. The ex didn't exactly hack into your girlfriend's doctor's files on her.
I believe that she feels put upon but there's no legal recourse for her on this particular issue. We live in days of shrinking privacy, and sharing information with anyone in any fashion risks that information being known to the world in very short order.
The ex doesn't owe her any kind of duty of care or privacy. If she wasn't pregnant then she could have a lawyer send him a "cease and desist" letter, although that would be difficult to follow up upon given that he lives in another country. Plus, she actually is pregnant so it's not like he has lied about her.
My best advice to your girlfriend is to stop worrying about what her ex is doing online. Too much drama is bad for her pregnancy, right?