There have been some recent studies on exactly this topic. The real difficulty is, with modern advances in medical sciences, ancient people groups experienced things we have names for, but they didn't understand underlying causes the way we do.

One recent study examined ancient Mesopotamian accounts and discovered behaviors that they attribute to PTSD in Assyrian warriors coming back from battle. (Abdul-Hamid, Walid Khalid, and Jamie Hacker Hughes. "Nothing New under the Sun: Post-Traumatic Stress Disorders in the Ancient World." Early science and medicine 19.6 (2014): 549-557.) (PDF Warning)

In this study, they discussed the fact that basically the entire adult male population was subject to military service every three years. A number of them suffered from symptoms they believed were caused by the ghosts of the enemies they had killed during battle, causing uneasiness and other symptoms. The authors of the study believe that if one of them were to walk into a clinic today and be diagnosed, it would be called PTSD.

They cite several examples of ancient Assyrian medical texts describing symptoms of people afflicted in this way:

14.34 “If his words are unintelligible for three days […]37 his mouth [F…] and he experiences wandering about for three days in a row F…1.”

14.35 “He experiences wandering about (for three) consecutive (days)”; this means: “he experiences alteration of mentation (for three) consecutive (days).”

14.36 “If his words are unintelligible and depression keeps falling on him at regular intervals (and he has been sick) for three days F…]”

Also,

19.32 “If in the evening, he sees either a living person or a dead person or someone known to him or someone not known to him or anybody or anything and becomes afraid; he turns around but, like one who has [been hexed with?] rancid oil, his mouth is seized so that he is unable to cry out to one who sleeps next to him, ‘hand’ of ghost (var. hand of […]).”

19.33 “[If] his mentation is altered so that he is not in full possession of his faculties, ‘hand’ of a roving ghost; he will die.”

19.34 “If his mentation is altered, […] (and) forgetfulness(?) (and) his words hinder each other in his mouth, a roaming ghost afflicts him. (If) […], he will get well.”

(I'm not sure which tablets these inscriptions come from, as they are not cited as I would expect, given that the article is a medical journal rather than an archaeological one)

Another example they cite is the description of the King of Elam (a Near Eastern polity located in western Iran) and how his "mind changed" after a war.

The really tricky part is whether these ancient stresses and reactions to the violence and brutality of war result in the same disorder as PTSD, or whether there are subtleties that make modern PTSD and the modern stresses that cause it a different ailment. We can't directly diagnose an Assyrian soldier haunted by the ghosts of the enemies he killed, so we can't answer that question, all we can do is interpret what they tell us about their lives in a framework that we can understand.

The article I cited above describes several other ancient accounts of afflictions resulting from battle stress, including a soldier who fought in the battle of Marathon, who suffered from blindness that appears to be psychosomatic in nature, resulting from psychological trauma suffered during the battle:

Epizelus, the son of Cuphagorus, an Athenian soldier, was fighting bravely when he suddenly lost sight of both eyes, though nothing had touched him anywhere – neither sword, spear, nor missile. From that moment he continued blinded as long as he lived. I am told that in speaking about what happened to him he used to say that he fancied he was opposed by a man of great stature in heavy armour, whose beard overshadowed his shield but the phantom passed him by and killed the man at his side. (p. 3)

Therefore, scholars believe we have depictions of mental illness similar to PTSD occurring during the time of the Assyrians, ~1300-600 BC.

Johnathan Shay's Achilles in Vietnam and Odysseus in America argue that both of Homer's epics have expressions of PTSD at their core.

Aristophanes is frequently on the perimeter. Some of his descriptions of phalanx combat or combatants, particularly in The Peace, but to a lesser extent in other plays definitely focus on those psychological effects. It's much more literary, but particularly with Aristophanes (as oppose to Aeschylus where there's a little of it as well) there's a certain finger-to-nose commentary about it.

Hi there, it looks like you have a couple of answers here already, which is great -- there's always more room for commentary on topics like this. You may be interested in the section of our FAQ that deals with PTSD in the premodern era -- we get a lot of questions on this!

Here's the relevant section: https://www.reddit.com/r/AskHistorians/wiki/war#wiki_post_traumatic_stress_disorder_before_the_modern_era

If you run into threads that are locked, please feel free to message the user (the format is like "hey /u/jschooltiger can you tell me more about ...") and they should get a username mention notification.

Thanks!