To the best of our knowledges, yes.

In scholarship on late medieval and early modern Europe, you'll often find the belief that Jews (men and women) in most of Europe were legally prohibited from owning or bearing weapons. This turns out to not quite be the case. Instead, laws communicated the idea that Jews were, as B. Ann Tlusty puts its, "not weapons-capable." As the special property/oversight of the king or emperor, they were legally guaranteed freedom from attack and molestation by Christians because they were supposedly unable to defend themselves. However, if Jews bore weapons, then the prohibition against attacking them disappeared. These laws both depended on and propagated the myth of Jewish men as weak, unable to protect themselves and their families, and effeminate.

On the flip side, Jews were expected to contribute to city and neighborhood defense just like Christians. Sometimes this meant "just" paying taxes and extra taxes, but frequently, yup, Jewish men were expected to don swords and knives and man the city or quarter gates.

Unsurprisingly, then, sources records Jews involved with weapons in basically every way Christians could be (including, Tlusty notes, a few ambitious merchants becoming international arms dealers). From Frankfurt, the primary focus of her study in The Martial Ethic in Early Modern Germany, she finds not just Jewish soldiers and mercenaries but--packaged just for you, OP--one Jewish man who asserted he was a Landsknecht who had served with his company in the Italian Wars (Solomon Ricco--Italian originally, as the last name suggests). And to answer the obvious objection, apparently he testified that his comrades absolutely did know he was Jewish.

The existence of Jewish Landsknecht raises a lot of logistical questions about how they were integrated into Christian units (I've not seen evidence for even groups of Jews serving together). Or: Jews were generally required to wear specially distinguished/marked clothing so everyone would know they were Jewish (and "protect" them properly, of course); the Landknechte of course are famous for adopting a collectively flamboyant style of dress. Where did Jewish Landsknechte fit in? Were they able to receive any kind of religous ministration while on campaigns? What about dietary differences?

So there's a lot that's up in the air, for sure. But the existence of Jewish mercenaries in the 15th-16th century is definitely not among those things--though not widespread, by any means, they are indeed documented as fighters for pay.