The animal was born just a few days ago in Rajasthan and it has an unusually flat face.
Owner Mukeshji Prajapap from the village of Nimodia, on the outskirts of Jaipur, shared a video of the rare creature in which it can be seen chewing and wagging its tail.
Local sources claim is it possible the goat may be revered as an 'avatar of God', with animals such as this often attracting a lot of attention in the country.
From a scientific perspective though, it is thought the goat suffers from a rare congenital defect known as 'cyclopia', where genes which under normal circumstances create facial symmetry fail to properly express.
Normally, the defect results in a miscarriage or a stillbirth, but the prognosis for the goat now is probably not good, as the condition causes the mouth and nose to form incorrectly, which can lead to eating and breathing difficulties.
Last year, a goat in the Philippines gave birth to an unusual-looking animal, which some have said looks 'half-human, half-pig'.
Farmer Josephine Repique, 40, from Sultan Kudarat, called in a vet to perform a caesarean section on her pregnant goat and they removed one healthy kid - however, the other one was pulled out to gasps of surprise.
It was born without fur and had shiny, pale skin with trotters and what appeared to be a belly button. It was also much bigger than its litter-mate.
Josephine said the animal 'looked like a pig with a mix of human'.
She added: "We were shocked. We can't explain how it looks like that. All our neighbours flocked into our house to get a good look."
Sadly, shortly after giving birth the mother and both babies died, prompting fears among some villagers that it was 'a cursed mutant devil'.
Josephine said: "Nobody knows what it is, but it's not a goat. It's scary. We're all wondering why it happened and if it is bad luck."
Of course, scientists didn't think it was some kind of devil curse, instead concluding that the animal was the result of some kind of genetic mutation.
Dr Agapita Salces, of the Institute of Animal Science of the University of the Philippines, said: "It is a possible case of genetic mutation. It is also possible that the mother contracted a disease called Rift Valley fever from mosquito bites and this caused the impaired development of the infant."