Police were called to the scene on Ferry Road Drive at around 1.45pm on Thursday after having received reports of a crash.
Several police vans, a fire appliance, and an ambulance attended the scene, where a car and a motorcycle collided.
Eyewitnesses also reported seeing armed officers patrolling a nearby area shortly after the crash happened.
The motorcyclist, a 24-year-old man, sustained serious injuries. He has been taken to the Royal Infirmary of Edinburgh for treatment. His condition is currently unknown.
Detectives have now launched an investigation after the occupants of the car fled the scene.
A spokesperson for Police Scotland said: “The occupants of the vehicle made off. Enquiries are ongoing to establish the full circumstances.
“Anyone with information, including dash-cam footage that could assist, is asked to contact Police Scotland on 101, quoting incident number 1820 of Thursday, 28 July.”
Emergency services remain on the scene and Ferry Road Drive has been cordoned off.
A green tent has also been set up on the street near where the crash took place.
Parents who were picking up their children from a nearby nursery reported that they were stopped by police and unable to get through.
Instead, they had to call nursery staff who brought the children to them via a safe route.
The Scottish Fire and Rescue Service has been contacted for comment.