This is a good question. It is best to start with a quotation from Aristotle's Poetics, in which he define what a tragedy is. He writes:
“Tragedy, then, is an imitation of an action that is serious, complete, and of a certain magnitude; in language embellished with each kind of artistic ornament, the several kinds being found in separate parts of the play; in the form of action, not of narrative; with incidents arousing pity and fear, wherewith to accomplish its katharsis of such emotions. . . . Every Tragedy, therefore, must have six parts, which parts determine its quality—namely, Plot, Characters, Diction, Thought, Spectacle, Melody.”
Based on this definition, Sophocles' Antigone is a great tragedy. For example, the tragedy, Antigone takes an action that is serious - life and death. It is also of a certain magnitude; royalty is in view. It also arouses fear and pity to create a katharsis. What can be more fearful than a young woman who goes against the ruler of Thebes knowing that she might die. She is finally sentenced to death and awaits death. In the end Creon, the ruler of Thebes has a change of heart, but it is too late. She hangs herself.
Antigone possesses many, but not all, of the elements of the ideal Greek tragedy as described by Aristotle.
In literary genre, it is clearly a tragedy. It has a Chorus and three actors. It is written in the appropriate meter and alternates between episodes and choral odes. It operates by means of mimesis, or imitation of action. Its earliest section explain the premise or dramatic situation, it has a central conflict, and it moves inexorably to an unhappy climax.
The main characters are noble, members of a royal family, and the action of the tragedy has "a certain magnitude", affecting the course not just of the lives of the individuals, but of the future of Thebes.
The reason why Aristotle, one suspects, uses Oedipus rather than Antigone, as his paradigm for tragedy is the problem of the tragic hero. In Antigone, one can consider Creon the hero and Antigone the antagonist or Antigone the hero and Creon the antagonist. Literary scholars have argued both sides of the issue. In both cases, we have noble characters whose stubbornness and pride leads to their downfalls.
But in view of the protagonist Antigone may not be a tragedy proper according to Aristotle as he urges the protagonist of a great tragedy be a male, not female like that of Antigone.