The City Bypass was closed eastbound near the Lothianburn junction from just after 8pm on Wednesday, until 3am on Thursday after the collision.
While Edinburgh City Road Police were assisting a driver who had broken down on the stretch of road, another car hit their vehicle.
Two male officers, from a unit based in Dalkeith, were injured, with one of them requiring treatment at the Royal Infirmary of Edinburgh.
Both the driver of the broken down car, and the driver of the other car were taken to hospital as a precaution.
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, 18 November, 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.
“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 re-opened around 2am.
“A report will be sent to the Procurator Fiscal and enquiries are ongoing.”