A black Land Rover Discovery was set on fire in Cairds Row in Musselburgh between 23:30 and 23:55 on Monday.
Police are appealing for witnesses to come forward.
Sgt Stuart Higginbottom, of Police Scotland, said: "Fortunately, no one was injured as a result of this fire but we are treating this extremely seriously."
Police are appealing for witnesses following a suspicious car fire in East Lothian.