Is it normal to "extract a paper" from a master thesis?
It is plagiarism only if you do not properly cite it.
If you have not published the thesis itself, of course you can publish parts of it or summaries of it or even the whole thing unchanged. The requirement to avoid "self plagiarism" is to cite. For example, in the introduction write:
This paper is taken from my thesis [title] done in [date] at [school] under the direction of [advisor].
It's totally accepted to publish journal articles based on thesis chapters. For one thing, MS theses are not well abstracted or searchable. Even with Ph.D. theses, they are rarely looked at. Getting something into a journal article is doing the scientific community a favor. It's also good for you and your coworkers in terms of pub count.
Consider the opposite--should one not publish any articles during grad school (to save them for the thesis)?
Just cite the thesis. That's sufficient. Nobody considers this double publication.
If you treat the thesis (and the other paper) like you would any other previously published work, then you avoid self plagiarism. In other words, cite the thesis as the source of the ideas and quote from it as necessary. Since it is also likely that you hold copyright on it, though maybe not on the published paper, you can quote more extensively from it than you might if it weren't your own work.
Self plagiarism doesn't mean that you can't restate your own ideas. It means restating them without indication of the original. The problem with self plagiarism is that it makes it difficult for a reader who wants the complete history of an idea to follow it back to the origin. The reason it is a problem is that the original contains additional context that the reader wants. The original itself normally cites other work and contains other ideas that form the context of the idea under examination.
Ignoring the plagiarism issue and answering only the top-line question, yes, it is normal to extract publications from theses.