The first two answers include valid examples of injustice within Frankenstein, and I believe that those examples demonstrate Shelley's struggle with her father's (William Godwin's) theory on morality--he believed that a human could control himself and his thoughts and eventually reach moral perfection. Victor and his parents (near the book's beginning) seem to demonstrate this view. When they see injustice, such as a once-wealthy child living in squalor, they right the wrong by taking her in and treating her as one of their own. Thus, through their striving for moral perfection, they justly respond to an unjust situation. Victor is brought up in this manner; so it is no wonder that he creates the monster without giving thought to his responsibility to the creature when it comes to life. He seems to have believed that the creature would be morally good and glorious and that he would not have to teach it about morality, justice, and fairness.
As Victor's relationships with the monster and his family/friends deteriorate; so does the standard view of justice. An innocent child (William) is needlessly killed by the monster; Justine (whose name means "justice") is executed for a crime that she did not commit; Henry is murdered, and then Victor is falsely accused of the crime. Shelley seems to be implying that while the idea of moral perfectioncreating a "just" world is noble, it is very difficult if not impossible to achieve because human arrogance gets in the way and results in injustice.
You can argue that Victor Frankenstein is a very unjust man in this book. You can argue that he shows, at least twice, that he is not willing to help cause justice to be done.
The first case is when he allows Justine to be executed for a crime she did not commit. He does this out of fear that people will think he is insane.
In a second case, though, Victor in unjust in his dealings with the monster. He acts as a judge, jury and executioner when he decides on what to do about the monster's request for a companion. In essence, he is telling the monster that it is evil and must not be duplicted. By doing this, he is setting himself up as the monster's judge. You can argue that he has no just right to do this.
In Shelley's Frankenstein, injustice is revealed mostly in the character of Victor. He not only creates a monster and fails to take responsibility for him, but then acts as judge and jury, condemning him even after the "monster," as Victor refers to him, tries to talk to him. And Victor, for the most part, rejects his creation based on appearance only.
Innocents also suffer in the novel. Justine is mistakenly condemned for a murder she doesn't commit, and again Victor has a hand in it. He not only creates the monster, but knows Justine is innocent and doesn't interfere. Elizabeth fights for Justine's life, but Victor does not.
Rejected by Victor, the monster, of course, kills numerous innocent people as well. Fairness and unfairness are in play from early on in the novel, beginning with Victor's first rejection of his creation.
Injustice caused by Victor is far-reaching in the novel.