I can't help but feel that the English translation should just be "she is an adult," or maybe "she is a grown woman." I can't think of any situation where I would use the phrase "adult woman."
I've changed the main translation to a grown woman, hopefully people will like it better that way.
'She is an adult' would be just Hon är vuxen in Swedish, there's a bit of difference in meaning. I don't think there's anything wrong with an adult woman either so that's still an accepted answer. Possibly it's more common in the US than in the UK. For instance I found a Vogue article with the title ”I’m an Adult Woman, and I Call My Mother Three Times a Day” http://www.vogue.com/13469579/why-i-talk-to-my-mother-three-times-a-day/
Of course 'adult' is often used in medical texts too, but you all know that.
'a mature woman' is in most cases en mogen kvinna
Re "she is a grown woman" You probably wouldn't say that in the UK, it seems to be an American expression. "She is an adult woman", or she is a grown-up woman" and most likely of all, simply "she is an adult" or she is a grown-up" would be a more British way of saying it
To me (British, in case that’s relevant) “adult woman” sounds absolutely fine, with very similar connotations to “grown woman”. E.g. parents discussing a daughter who’s left for college: “She’s not a girl any more, she’s an adult woman.”
Edit: for those disagreeing, see e.g. this chart comparing usage in the Google Books British English corpus. It shows that an adult woman occurs roughly around half as much as a grown woman — less often, but quite often enough that it’s a genuine widespread usage not an error.
Agree. A woman is an adult human female. I've never heard of anyone using adult woman before. It's not necessary to have adult there at all. Mature woman (as mentioned below) is fine.
Mature woman to many implies old! In clothing ranges/sizing mature certainly does.