Their car, which had its blue lights on, was in collision with a Volkswagen Polo on the M8 near Bishopton, closing the road for hours and causing rush-hour chaos .
Both vehicles were travelling west when the accident happened at about 3:30am between the Erskine Bridge turn-off at junction 30 and junction 31 West Ferry, Renfrewshire.
As yet it has not been explained how the crash occurred or why the police car had its blue flashing lights on.
Though injured, the two Strathclyde policemen involved managed to walk away from the wreckage.
Both were taken to Paisley's Royal Alexandra Hospital for treatment but were later released. One officer suffered minor injuries to his neck and shoulders and the other required 21 stitches to his left arm. The 27-year-old driver of the VW Polo was also taken to the hospital but was found to be uninjured.
After the accident, the road was closed for about six hours, causing major disruption on city roads until mid-morning.
Although the police car had its blue lights on, it was not responding to an emergency call.
Police are investigating why the car had its blue lights on, but it is not thought it was pursuing the other vehicle involved in the collision.
Last night, a spokeswoman for Strathclyde Police said that the cause of the crash was still being investigated. "Inquiries into the cause of this incident are at an early stage, however can confirm that officers can use lights for other purposes than attending emergency calls," she said.
Neil Greig head of policy at the Institute of Advanced Motorists, said of the incident: "Essentially, police are often involved in manoeuvres that other drivers aren't, so you would expect them almost to have more accidents and we are not particularly critical of the police in this regard.
"What we are more concerned about is the length of time spent investigating crashes such as this morning's, which was a two-car collision involving relatively minor injuries.
"Perhaps it was because it was a police car that it took longer and, of course, it all needs to be done accurately, but the time taken to investigate actually causes more disruption than the crash itself."
The incident comes just weeks after a police car, with lights flashing and siren blaring, struck the central barrier while heading south on the M77 near Silverburn, Glasgow.
In a separate incident yesterday, motorists on the M8 near Livingston endured three-mile tailbacks after a three-vehicle crash.
The accident happened at about 7:10am on the eastbound carriageway, one mile east of junction three near Livingston. There were no injuries and traffic was moving again by 8am.