The driver continued south on Gilmerton Road and the car was later found abandoned a short distance away on Glenallan Drive.
Police Scotland said they were following a positive line of inquiry.
Sgt Grant Hastie said: “Our inquiries are ongoing to establish the full circumstances and trace those responsible.
“I would urge anyone who witnessed the crash, or saw a blue Vauxhall Corsa in the area beforehand or afterwards, to come forward.
“We are also keen to speak to anyone, external with dash-cam or private CCTV footage that may assist our investigation.”
