I would suggest that the irony is situational but that it isn’t intended to be humorous at all.
Brutus originally agrees to join Cassius’s and the conspirators’ assassination plot against Caesar because Brutus truly believes it is for the good of Rome. However, Brutus eventually discovers that Cassius deceived him and that Caesar’s death has only plunged Rome into utter chaos. Thus, Brutus’s actions actually had the opposite effect of what he intended.
He is wracked with guilt over this, as evidenced by Caesar’s ghost visiting him before the battle at Philippi and by his quarrels with Cassius. When Brutus realizes the battle is over and he is on the losing side, his suspicions that he should never have killed Caesar are confirmed. He interprets the military loss as a sign that he was in the wrong. Therefore, when Brutus decides to take his own life, it is because he sees himself as a danger to the country he loves.
The irony, then, is that Brutus killed Caesar for the good of Rome, but instead he only made Rome one step closer to the totalitarian regime that he’d hoped to avoid. He is then forced to take his own life, because he feels responsible for the downfall of Rome.