In the video, a car can be seen mounting the pavement and striking the victim in Mansfield town centre.
Nottinghamshire Police said it was "unbelievable" he suffered only minor injuries and is "recovering well" after the incident, which happened in April.
Officers are appealing to garages which may have repaired a Skoda Octavia with front end damage.
The victim was hit in Leeming Street by a dark-coloured vehicle, which also collided with an electric box before heading off along a bus lane and travelling down Clumber Street.
Police believe the car was parked in Leeming Street before the incident and the driver may have been involved in an altercation with people outside the Bowl in Hand pub.
Det Con Kelly Holloway said: "Had the car not struck the electric box this incident could easily have ended in tragedy."
Footage of a hit-and-run in which a man appears to be crushed against a wall has been released.