The Copyright Act doesn't extend its protection to nonhuman animals, says U.S. District Judge William Orrick.
Of course, a monkey wouldn't know he had legal rights even if he did. Some human beings would need to purport to represent the monkey, and that's what was going on here. People for the Ethical Treatment of Animals sought to capture the income stream from Naruto the monkey's beloved photography and offered to spend the money for the benefit of him and the various other crested macaques on the island of Sulawesi.
Here's the beloved and apparently uncopyrightable monkey selfie:
Naruto is delighted with the public domain.
ADDED: Here's an earlier post about why the copyright isn't seen as belonging to the man who set up the camera, setting up the conditions and predicting the last step, a monkey's pushing the button.