The fire service were called to Dean Terrace in the Stockbridge area at about 03:00 on Sunday.
The cars, a BMW 116d and a red Mercedes 220 CDI, were found to be well alight. Police believe the fire was deliberate.
No one was injured in the blaze but officers said they were "keen to hear" from anyone in the area who saw anything suspicious early on Sunday.
Det Con Douglas Mogg said: "Both cars have been completely destroyed by the fire, which appears to have been started deliberately.
"Witnesses in the area heard a man talking with a local accent at around 2:45am followed by a loud bang and then flames coming from the cars.
"I am keen to hear from anyone who was in the area of Dean Terrace around this time to please contact police on the 101 number or speak to any officer."
Police in Edinburgh have appealed for information after two cars were set on fire.