The dog is believed to be a Staffordshire bull terrier, or a Staffordshire cross.
Because of the extent of the dog's injuries, it is not known at this stage what colour its coat had been, the BBC reported.
The gruesome incident happened in a wooded area in the north of Kirkcaldy in Fife on Friday, police said.
A post-mortem examination is to be carried out as part of Police Scotland's investigation into the dog's death.
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"Anyone who is familiar with someone who had a dog such as this but has not seen it for a few days or who saw someone in the north Kirkcaldy area with a dog and a green petrol container is asked to contact us on 101.
"I have little doubt that most people will be horrified at what has taken place and anticipate a strong response from the public. I would also urge whoever is responsible to contact the police," Laing said.
"It is unimaginable that anyone could be involved in such a cruel premeditated attack on an animal. This poor dog appears to have been killed in one of the most barbaric ways possible," Flynn said.