The PC stopped the car in Gaugemaster Way in Ford, West Sussex, at about 08:00 GMT after receiving a report that it had been stolen in Wiltshire.
He was caught in the door after the car reversed and was dragged along before being “thrown free”, a spokesman said.
The car's driver and passenger were arrested in Yapton shortly after.
The Sussex Police spokesman said the car had been followed across West Sussex after it was spotted in Emsworth at about 07:15.
He said that after the officer was freed from the car, it had driven off, ramming a police car in the process.
He added that the injured officer was treated at St Richards Hospital in Chichester for “cuts and bruises” before being allowed home.
Ch Insp Tanya Jones said the PC had been “very lucky not to have been more seriously hurt”.