The footage shows a woman taking off her shoe and hitting a car windscreen with it before someone jumps inside the vehicle and it suddenly lurches forward.
The woman is knocked to the ground as she clings on to the driver-side door and the car narrowly misses a man standing on the pavement.
The male pedestrian then chases after the car, attempting to wrench open the driver’s door before it hurtles towards him and knocks him to the ground.
Footage of the incident, which took place at about 9pm on Saturday in the Bigg Market area of Newcastle, had been shared more than 43,000 times at the time of writing.
Northumbria Police said it was investigating after receiving reports of a fight “involving a number of individuals” in Groat Market.
The force said in a statement: “Following a disagreement in the street, an offender then entered a vehicle and drove it at a man, knocking him to the floor.
“The occupants of the car then made off from the scene.
“An investigation is ongoing into the incident and officers are now carrying out enquiries to trace those involved.”
Acting Inspector Michelle Jahangiri said: “This is a very serious incident that happened in a very busy street in Newcastle city centre.
“This could have resulted in a very serious injury, and I would like to reiterate that this type of behaviour is totally unacceptable and will not be tolerated.
“We are aware of footage circulating on social media regarding the incident, and would ask members of the public to respect the ongoing investigation.
“Officers are the process of identifying the victims and offenders involved, and will take robust action against anybody found to be involved.”
Anyone with information about the incident is asked to contact 101 quoting reference 1160 270719 or Crimestoppers anonymously on 0800 555 111.