The pair stopped between the Lothianburn and Straiton junctions of the A720 at 8pm on Wednesday when a third car hit their police vehicle.
One officer, who was on the roadside, suffered leg injuries and was taken to the Royal Infirmary of Edinburgh.
The second officer, who was inside the police car, suffered an arm injury but did not require hospital treatment.
Inspector Roger Park, of Edinburgh City Road Policing, said: “Two officers were injured while attending a broken-down vehicle on the A720, Edinburgh City Bypass, between the Lothianburn and Straiton junctions around 8pm on Wednesday, November 18 2020.
“While the male officers from the road policing unit based in Dalkeith were assisting the driver, another car collided with their vehicle.
“One officer, who was not inside the car, sustained leg injuries and was take to the Royal Infirmary of Edinburgh by ambulance and released later.
“The other officer sustained an arm injury but did not require hospital treatment.”
He added: “The driver of the broken-down car and the driver of the other car were both taken to hospital as a precaution.
“The road was closed eastbound and reopened around 2am.
“A report will be sent to the procurator fiscal and inquiries are ongoing.”
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