The accused driver, Biru Prasad Yadav, a native of Uttar Pradesh, was arrested and he was found drunk, they said.
Traffic Constable Yashbir Kumar was on duty near the Palla Traffic Signal on National Highway-1.
The accident was reported at 12.30 am on a road where the traffic police have restricted plying of heavy vehicles as wedding processions pass through the stretch, the police said.
The constable was declared brought dead at a hospital here, they said.