The collision took place in Aldersley Road, just after 6.30pm on Friday.
Photos from the scene show a white vehicle reversed against a wall on the busy street. They also show damaged metal and plastic fencing along the wall.
It is believed a black Seat Leon approached a white Seat Leon in the street, which then reversed into a wall and an altercation took place.
No injuries were reported during the collision and police are urging anyone with information to come forward.
A spokesman for West Midlands Police said: "We received a report of a car crashing into a wall on Aldersley Road, Wolverhampton just after 6.30pm on Friday, July 23.
"A black Seat Leon has allegedly approached a white Seat Leon, which then reversed into a wall and an altercation has taken place. There were no reported injuries.
"Anyone with information is asked to contact us."
Witnesses can call West Midlands Police on 101, quoting log number 3647 of July 23.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org