Two large bags of brown powder were discovered inside the house on Magdalene Drive at about 4:30pm on Monday.
Police are now hunting the former occupiers.
The raid was part of Operation Adrenalin, an ongoing police action to tackle the drug trade in the Capital.
Approximately 400 grams of heroin were recovered with an estimated street value of 40,000.
A police spokesman called for public assistance in tracking down the suspected dealers.
"Once again, we have identified and targeted individuals concerned in the supply of drugs and shut down their operation," he said. "We are now eager to locate the occupants of this property and would urge local residents who may have information to contact police immediately.
"Similarly, anyone with information concerning drug-related criminal activity in their area is also asked to come forward."
This latest sting takes the total value of narcotics taken off Edinburgh's streets to 70,000 since Operation Adrenalin was launched in January. Drugs seized include heroin, cocaine, crack cocaine, cannabis and prescription medicines.
Almost 10,000 in cash has also been recovered.
Officers have also seized three complete hydroponics systems, irrigation devices used in soil-less cannabis cultivation.
As part of the operation, 34 people have been charged with various drugs charges.