I'd say it is increasingly uncommon.

For the study of the medieval world, degrees represent not just a milepost in the developing tools of interpreting evidence, but also the learning of skills to access that evidence—languages, paleography, manuscript studies, etc. I can think of prominent medieval historians without doctorates whose publications are still well regarded, but they are from a previous generation. For example, Eric Christiansen proposed a doctoral thesis that Oxford rejected, but subsequently held a lectureship there and wrote a rather well regarded book on crusading activity in northern Europe. But, there as in elsewhere, these are individuals who may not hold a PhD but remain deeply embedded within the academic world.

That said, while possessing the skills to do the work of history without a graduate degree would be unusual, I don't know of a journal in the Medieval academic world that has rule explicitly prohibiting the publication of a piece because its author lacks a degree. That is, as long as the submission has met the submission criteria and does well under peer-review. I do know of a few journals that require a PhD to review books, but I believe that has more to do with the economics of sending out review copies more than anything else.

I wonder how say, an American historian, would respond to this question.

To try to bring together what /u/Gaimar and /u/LegalAction said:

It depends on what you mean by "published." If you mean in the narrow, academic-world sense as Gaimar interpreted the question--probably not, unless you're an undergrad publishing in an undergrad-only journal. If you mean in the "my book might be at Barnes & Noble if it's really successful" sense, sure, why not.

Academic publishing in journals is usually double-blind peer review, although in some cases a specialty is so small that the reviewer (for potential publication) may well know or suspect the scholar's identity. Still, there's no immediate credential involved in a lot of cases, at least at the initial review stage, although presumably it could enter in later.

However, there are a lot of implicit barriers to someone without the day-in, day-out experience of reading and writing and reading and reading in an MA/PhD programs when it comes to academic publishing. There is a language to the field even if it doesn't rise to the level of jargon, but more than that, there's the sense of "what/who you have to cite" and when you cite things that kind of has to be absorbed, not taught.

There's also the matter of access to academic library resources--so being a current grad student, early career researcher, or professor--but there are ways around that.

The popular history publishing game, however, is quite different. We've had multiple academic historians on AH say they've tried to publish pop stuff, but have turned away for a lot of reasons. Sure, of course you'll find many PhD credentials on the bookshelves and on Amazon. But for better or worse, there's also plenty by people with bachelor's in history, with vast experience in journalism, with degrees in English and creative writing, anthropology, science, what have you. Alison Weir has no graduate education at all (and she has published in medieval, albeit very late medieval). Charlotte Gordon has a PhD in literature. Erik Larson has a master's in journalism and one of his books is in development as a big-studio movie.

Make no mistake, grad school gives a LOT of advantages in terms of knowledge base, experience with primary and secondary sources, and up-to-date information on topics just now being explored. It gives you time to learn. And if you want to publish the kind of articles and books that AskHistorians writers typically cite, it's probably a tacit necessity.

But if you want to write awesome things that people enjoy reading, it could certainly help but lacking a history ed is no deal-breaker.