No, in medieval Europe, there were no restrictions on common soldiers killing a king or any other aristocrats. If soldiers were able to identify a particularly important individual, there would probably have been a mad scramble to capture him rather than kill him outright, both for political purposes and for the potential for ransom profits. This happened to the French king Jean II at Poitiers, who was taken prisoner in a furious melee where other high-ranking French aristocrats, who ordinarily would have made excellent ransoms, were killed (possibly by accident as English troops swarmed to grab Jean specifically). When kings were killed outright in combat, it does not seem to have been a particular mark of controversy. John the Blind, King of Bohemia, died at Crecy but his killer was not specifically identified in accounts of the battle and the story of his death is conveyed merely as an illustration of John's bravery and valiant nature. Kings who fought did so in the full knowledge that they were at risk of being killed or captured at the battlefield.

English military contracts from the Hundred Years War suggest that there was no stigma attached to a common soldier capturing important aristocrats; they often contained clauses saying that any particular important prisoners (like a prince or something) would be handed over to the king in exchange for a cash payment. This worked to both parties' advantage: common soldiers would probably not be be financially able to house and feed a prisoner (especially a royal prisoner) during the period in which the ransom was negotiated and paid. If there was any limitation on killing aristocrats, it would be that troops wanted to maximize their profit by taking nobles alive for ransom. This is most apparent in the hesitation of some English troops to kill their prisoners at the Battle of Agincourt. This incident is often taken as some kind of commentary on class relations, but in reality is just a reflection of soldiers looking out for their bottom line.

Do you have a “where” or “when” to your question? You’re much more likely to get a satisfying answer if you include that in your post.

As a follow up, how did the nobility fit into this hierarchy? It is my understanding that hostage/ransoming took place, but how extensive was this and how did one's social status fit into the realities of battle?

Plutarch reported that two soldiers were executed in gruesome fashion after taking credit for killing Cyrus.

I've wondered, however, whether this was officially stated as for fraudulently claiming to have killed someone that Artaxerxes did, or merely for saying anything to the detriment of his reputation? Or did Artaxerxes not bother to give a reason? It doesn't seem from the way it's written that there was supposed to be anything wrong with them having killed Cyrus, just that Artaxerxes didn't want to give credit (and was this because it was "proper" for him to have done it, or just generally desiring glory?). Was this story known at the time? Plutarch says no one saw his death but seems strongly to credit the account of Ctesias.