The apartment in Constitution Street, between the junctions with Bernard Street and Tower Street, was broken into earlier this week.
It was raided sometime between 10am on Saturday and 9am on Tuesday but officers working the case believe the break-in may have happened around 10pm on
A large metal safe, containing cash in both pounds and dollars and distinctive pieces of jewellery, was found to have been stolen.
PC David Smith of Edinburgh’s Community Investigation Unit said: “The contents of the safe are believed to be collectively worth a six-figure sum and this is currently being treated as a targeted theft.
“The stolen safe weighed over thirty stone and is likely to have taken several people to move and, we believe, may have been take from the property in another item, such as a suitcase.
“It’s likely that a vehicle was involved to transport the safe and we’d urge anyone who may have seen suspicious behaviour, or vehicles, in the area around this time to contact us as soon as possible.”
Anyone with information can contact police on 101.