There are a couple of candidates for this answer, but perhaps the clearest moment of anagnorisis in Macbeth occurs at the end, in the final scene, when Macduff informs Macbeth that he was "from his mother's womb untimely ripp'd." At this moment, Macbeth learns that the witches' prophecy is about to come true, and that he will die at the hands of Macduff. He fully recognizes this fact, saying that it has "cow'd my better part of man," he initially refuses to fight Macduff. Of course, he has already learned, in what could also be called a moment of anagnorisis, that Birnam Wood is advancing on the castle, which the witches also say is a harbinger of his death. But it is at the moment when he realizes that Macduff was "not of woman born" that he really knows his death is near.
Anagnorisis originates from Greek and occurs when, in fiction, a character, a tragic hero, makes a critical discovery both about himself and the person he has become. In Macbeth, this comes when Macbeth fails in his plan to secure his position as king in the long term.
Macbeth meets the criteria for a tragic hero. At the beginning, Macbeth is brave and valiant and has defended his king to such an extent that he will receive the title Thane of Cawdor in recognition of his efforts. Therefore his noble stature is acknowledged. As the play proceeds and the plot develops, the audience recognizes his conflicted nature and can relate to his struggle with himself. For example, he tries to quell his "earnest of success," in Act I, scene iii, line 132 and later tries to talk himself out of any disloyalty to Duncan which he knows is due to his "vaulting ambition" (I.vii.27). Ultimately, having made his decision to "proceed no further in this business" (30), Lady Macbeth then shames him into going ahead with Duncan's murder by questioning his manhood and therefore his dignity. The audience then pities him. However, he does ultimately make the decision and is accountable for his actions. Macbeth's fatal flaw, his overriding ambition, subsequently drives him further than even Lady Macbeth ever envisioned for him. This will ultimately lead to his downfall, a requirement for a tragedy of this nature as a Shakespearean audience must leave the theater with a sense that wrongs have been righted. In Macbeth, the rightful heir will take the throne.
Accordingly, there is a moment of anagnorisis when Macbeth realizes that his efforts have been futile. However, realization has come too late to save Macbeth and he will die. His conscience has taken a long time to catch up with him but it has and his subsequent deeds are those of a desperate, even delusional man but one who is aware that the "juggling fiends" (V.viii. 19), the witches, have taken advantage of him. He engenders more pity.
Depending on interpretation and questions raised as to exactly when Macbeth realizes that he is doomed, Macbeth's anagnorisis could be said to occur in Act V, scene v when he becomes aware of Lady Macbeth's death. His understated reaction could indicate his complete exhaustion and defeat together with a involuntary awareness and his comments that life is nothing more that "A tale, told by an idiot...Signifying nothing" (26-27) mark a significant moment. Nothing is worthwhile anymore so why not keep going blindly anyway?
It could also be interpreted to occur later as, after her death, he continues in his quest not to be beaten, indicating that anagnorisis could come when the witches prophecies are used against him.