This sounds like a yeast issue to me. Wild yeast contamination can sometimes occur in bread factories after baking, and some of them can produce acetone (or similar smells). Salt also acts as a preservative in inhibiting growth like this, so a salt-free bread may be more prone to such growth.
Acetone notes are sometimes found in sourdough cultures (usually ones that aren't growing well). It would also not surprise me to find such odors in sprouted grains. Some of these odors can stay in the bread even after baking. And it's possible that the outer layers of the bread may have offgassed those odors during baking, but the stuff from the inner layers works its way out over several days after the bread is bagged. If that were so, though, I'd expect the bread to taste odd too, with acetone or organic chemical notes.
As for safety, it's tough to say. In most cases this would indicate contamination or at least something unbalanced in the bread production. I personally would discard it, and if I encountered another loaf from the same manufacturer with the same characteristics, I'd consider contacting them to see if they can explain it (or, if not, that they're at least aware of the problem).