The ornate urn was discovered at 2am on Sunday, April 30.
In a Facebook post, the force said: “So far, no one has come to claim the item and so through the power of social media we want to ensure it’s returned to its rightful owner.
“The urn is within a small velvet box and is dark grey and white in colour. Please share our appeal so whoever lost it knows we have it. If you are the owner of this urn then please come to our Lost Property Dept at Fettes Police.”