The horrific incident occurred in a woods in Kirkcaldy, Fife and it is undertood that the animal was doused in petrol before being set alight.
The dogs charred remains were discovered in the woods in the north part of the town on Friday.
Police said it was a “gruesome scene”, and animal welfare workers described the manner of its death as “barbaric”.
The dog had been tied to the tree, doused with “a flammable liquid” and had been set on fire.
It is understood that the dog was probably a Staffordshire terrier or Staffordshire-cross, but it was too badly burned to ascertain what colour its coat had been.
It will undergo a post-mortem examination by a vet today.
PC Ian Laing, Wildlife Crime Liaison Officer for Fife Division of Police Scotland said: “It is clear that this dog died in horrendous circumstances and will have endured considerable pain immediately prior to its death.
“It is essential that the public assist us in identifying who is responsible for this. 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 or through Crimestoppers on 0800 555 111.
“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.”
Scottish SPCA Chief Superintendent Mike Flynn said: “This is an extremely sickening case of animal cruelty and we are keen to find those responsible for this dog’s painful and violent death.
“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.
“We would urge anyone with any information to contact Police Scotland on 101 or the Scottish SPCA on 03000 999 999 as we will work alongside police to ensure that those involved are caught.
“It is also vital that anyone whose dog fits the description and may have gone missing in the area, gets in contact with police or ourselves.”