The incident occurred at around 1.30 PM when head constable Yogendra, deployed with a traffic police interceptor, tried to stop the speeding car on Pushta road near Shamshan ghat area, a senior police official said.
The driver of the car, identified as 18-year-old law student Nikhil Kumar, instead of stopping the car hit the constable, flinging him away.
The injured constable was rushed to LNJP hospital from where he was shifted to a private hospital for treatment of his critical injuries, the officer said.
Nikhil lives in Geeta Colony and is pursuing a Law course from an institute in Sahibabad, they said.
Last month, a 32-year-old marketing executive Siddharth Sharma was killed while trying to cross a road in central Delhi's Civil Lines area when he was hit by a Mercedes driven by a juvenile.