ETA: The most neutral way to say this sentence is just as it appears in your post, without an article at all:
Mrs. Jones has been selected for the post of principal.
There is no added meaning here. You are just conveying the fact that Mrs. Jones was chosen for the position. (/edit)
If you were to say:
A Mrs. Jones has been selected for the post of principal.
the emphasis is on the fact that you know nothing about Mrs. Jones other than her name. You should be a little careful with this construction. Especially when you are talking about someone who was selected for the position, it could give your audience the idea that you aren't sure whether they are qualified. Nothing is known about their prior experience. Are they qualified? Of course, that may be exactly what you are trying to get across!
On the other hand, if you were to say:
The Mrs. Jones has been selected for the post of principal.
then you are implying that Mrs. Jones should be well-known to your audience, and that even though there might be many people out there with the name Mrs. Jones, the well-known one is the one who was selected.
This might be easier to understand with a more famous name. For example:
Our school is having a talent show. We've gotten the Simon Cowell to judge the show.
Here, you want to emphasize that the famous talent scout is the one who will be there, not some other guy who just happens to share the name.