The incident happened on Broomhouse Street North at about 18:15 on Wednesday.
Detectives said there was a disturbance involving a group of men, some inside the vehicle and some on the road.
One man was seen to pursue a small black car and hit it with a pole or similar object, causing some damage.
Officers are urging anyone with information to get in contact.
Det Insp Roddy Hardy, of Police Scotland, said: ""We believe this was a disturbance involving a group of males, some inside the car and some on the road, and we are keen to establish their identities.
"We are especially keen to speak to the man who chased the vehicle as he may know the identities of those involved and assist us to trace them.
"Anyone who witnessed this disturbance of who has information that can help us trace the individuals involved is asked to contact police on 101 or anonymously via Crimestoppers on 0800 555 111."
Police are trying to trace a man who chased after a car in Edinburgh and struck the vehicle with a pole.