The driver of the car, identified as Ravi, after hitting the bike, dragged it till about 100 meters before fleeing from the spot. He is yet to be arrested, police said.
The injured personnel have been identified as Manoj Kumar (37) and Shivani (23) who are posted at Mayur Vihar police station, they said, adding that the duo has been shifted to a hospital where their condition was stated to be critical.
The incident happened late night yesterday when the police personnel were returning to the police station on a motorcycle after their duty at a Ramlila event.
A case of attempt to murder and negligent driving has been registered against the accused, he said.
The car involved in the incident was later found abandoned at Ashok Nagar area, police said, adding that the vehicle was registered in the name of the accused's mother and has been confiscated.
The injured Manoj is a resident of East Vinod Nagar area in east Delhi while Shivani lives in Kotla area.