The charity was alerted after a member of the public made the discovery at Cemetery Lodge in Howe Road on August 16.
The older cream-coloured female is thought to be a Lhasa apso or similar breed. She was not microchipped or wearing a collar when dumped between the evening of August 14 and 3pm on August 16.
Scottish SPCA inspector Robyn Myszor said: “We’d like to find the owner and find out how she came to be in the bin at the cemetery. This is not the proper way to dispose of an animal who has passed away.”
Anyone with information should call 03000 999 999.