It causes genes which, under normal circumstances create facial symmetry, fail to properly express.
But some residents in remote Nimodia have been worshipping the animal, reports suggest.
In India, it is common for such animals with rare conditions to attract a great deal of attention.
Footage shared online shows the goat stumbling and wagging its tiny tail.
Typically one in 16,000 animals is born with cyclopia, which also affects humans.
When a mutant calf was born in Argentina last month with a small nose and mouth and resembled a grumpy human face, vets were stunned and desperately tried to help it.
But it died after just a few hours in Villa Ana in the north of the country.
And in November last year, a bizarre-looking fish with what seemed to be a human face complete with a nose, two eyes and a mouth was spotted in a Chinese lake.
Footage showed the creature swimming towards the back of a lake in Kunming on November 5, and while its body matched the standard description of fish, its head looked human-like.
