The Greek word eironeia originally meant something like a fake or fictional ignorance. Aristotle (NE IV.7 1127a-1127b) uses it to describe a vice of defect opposing both the virtue of truthfulness about oneself and the excessive vice of boastfulness (alazoneia). It is not as blameworthy a vice as boastfulness, since the self-deprecating will tend to come across as more civilized than the boastful, but deliberately telling falsehoods is in itself an ignoble thing. He also speaks briefly of it in the Rhetoric (II.2 1379b, 1382b), noting that we tend to get angry at the ironical when we are being serious, because we interpret it as a sign of contempt for us, and also that the ironical can be something to fear because you can never be sure how close they are to doing something harmful to you -- they hide their real attitudes. On the other side, though, he also emphasizes the apparently civilized character of eironeia, because the ironical man tends to jest at his own expense rather than the expense of others.
Theophrastus in his Characters describes eironeia as "affectation of the worse in word or deed". The picture he paints is of a very dishonest man, the sort who treats his enemies as if they were friends -- to their faces, at least -- and who will never commit to saying what he is actually doing, hiding under the excuse that he is only thinking about things.
Aquinas's account of the virtue of truthfulness is much more expansive than Aristotle's, which was primarily about oneself, but he stays closer to Aristotle in describing the vice of ironia (ST 2-2.113), as it comes out in Latin. It is in some way saying something lesser about oneself. The act of saying lesser things about oneself than are strictly true could be done salva veritate, as a way of appropriately concealing one's greater qualities in a context in which they would distract from what is important; but the vice of ironia concerns cases in which one falls away from the truth, as when you attribute to yourself a failing you don't actually think you have, or when you deny something great about yourself that you are confident you do have. Such falling away from the truth is a kind of mendacity and is intrinsically wrong. Aquinas argues that Aristotle's ranking of irony as less bad than boastfulness is a matter of the usual motives behind them: the boastful are more likely to have a base motive of grasping after money or honors than the ironical are. Nonetheless, it can, he insists, be the case that irony is worse than boastfulness if its motives are worse.
Since ironia opposes truthfulness, which is a potential part of justice and thus a kind of justice-in-a-broad-sense, its wrongness constitutes a form of injustice -- against oneself, one assumes, although perhaps also indirectly against any kind of good, since it involves depreciating and obscuring good for one's own ends.