The car's driver Akhilesh Lohia, 36, was arrested from the spot. He was inebriated at the time of the incident, they said.
Lohia was returning from a marriage party and was allegedly speeding. Constable Bhoop Singh, 34, who was deployed at a police picket for checking vehicles, had signaled the driver to stop, the police said.
Singh was posted with the Vasant Vihar police station and was on night duty. He suffered a severe head injury.