The discovery was made in north east Fife yesterday, Police Scotland said.
The force said inquiries are currently at a very early stage.
Forensic experts are examining the remains and the location.
The discovery comes as police search for Susan Reid, who has been missing since January.
The 56-year-old is from Newport on Tay in north east Fife.
Police said her disappearance is still being treated as a missing persons inquiry and asked anyone with information to come forward.