As has been noted elsewhere, “The Happy Prince” is told from a third-person omniscient viewpoint. Given what happens in the story, this is entirely appropriate. Because if there's one thing we learn from reading the story, it's that the characters involved have very different ways of seeing the world.
Whether we're dealing with the mayor and other local worthies, the poor people of the town, or the Happy Prince himself, we have a multiplicity of perspectives of which it's only really possible to make sense by the use of an omniscient, third-person narrator.
Though we never learn the precise identity of the narrator, he does enjoy a God's-eye perspective on things. As well as seeing everything that goes on in the town, he can see inside the souls of statues, people, and animals alike, developing an intimate awareness of their feelings. It's as if the narrator had himself created everything he describes. The comparison with God, though by no means definitive in determining the narrator's identity, is nonetheless suggestive.
Whether the narrator is God or just Godlike, he gives us the broadest possible perspective on the town in which the action takes place and those who live there. It is this perspective that makes the town more recognizable as a place in which real people live, instead of the kind of fairytale world that fables often present to us.
In political terms, the third-person omniscient narrator gives us a chance to see the desperate poverty in which so many people in the town are forced to live, giving Wilde the socialist a chance to say something important about the enormous gulf that existed in his day between the haves and the have nots. Closing this gap and alleviating the appalling plight of the poor requires the kind of comprehensive vision that only a third-person omniscient narrator can have.