The incident happened in the Sighthill area of Glasgow at about 13:00 on Tuesday.
The officer had been speaking to the driver of a red Vauxhall Astra when he suddenly threw the car into reverse.
He then got out of his car in Alford Street and fled on foot. The police officer was unhurt.
A Police Scotland spokesman said: "The officer did not require medical treatment and resumed duty following the incident. The man in the car then ran off.
"Police are following a positive line of inquiry."
The Scottish Police Federation has been made aware of the incident.
An attempted murder inquiry has been launched after a driver reversed, dragging a police officer down the street.