I'm in the 'tell her' camp. People always say don't tell because the person ends up hating you. I get that, but the alternative is to not tell and let them be in a bad relationship and waste who knows how long of their life with a loser. I'm willing to let them hate me in order to preserve their ultimate well being.
However, I think playing dumb might be the key- it makes it less of a big, huge deal. Next time you see her, say "I heard you and X are breaking up, I'm so sorry". When she asks what you are talking about, just say "oh, I heard from our mutual friend that X was dating someone else and told her you broke up". Depending on her reaction, you can just move on. If she freaks out, be there for her while she pursues information. If she tries to dismiss it, then say "wow, I feel so silly, I must have heard it wrong". She'll process the info and what she does with it then is up to her.
Good luck.