The South Yorkshire Police firearms officers were on routine patrol when they saw a car which had stopped in a live lane between junction one of the M18 and the M1 link road, just after 9.30am on Sunday, April 18.
The officers approached the car - a grey BMW 3 series - and noticed the driver appeared to be unconscious.
Acting Inspector Tom Fisher said: "Officers believed the driver had suffered a medical episode at the wheel and therefore forced entry to the car. At this point, the car suddenly reversed and collided with the parked police vehicle.
"As a result, the two officers were forced into a live lane of traffic, before the vehicle left the scene."
A short time later, traffic officers located the car again, stationary in a lane at junction 33 of the M1.
The driver, a 45-year-old man from Doncaster, was arrested on suspicion of failing to stop for police, assault on an emergency worker and being unfit to drive through drink or drugs. He has since been released under investigation.
The officers involved in the incident suffered minor injuries.
Anyone with information is urged to call police on 101, quoting incident number 274 of April 18.