The incident occurred near R.K. Khanna Stadium in south Delhi around 1 a.m.
The speeding truck, going towards Naraina, first rammed into a WagonR car, then hit an Eeco car which overturned due to the collision killing a person, a senior police officer said.
After hitting the two vehicles, the truck rammed into the barricade where the constable on duty was crushed to death, the officer said.
Additional Deputy Commissioner of Police Nupur Bharadwaj told IANS: "Police Constable Deepak, and Santosh Baro, died on the spot after the truck hit the barricade and two vehicles near the police picket."
"The two injured persons were identified as Asper and K.S. Sura. They were rushed to hospital," the police officer added.
Despite the string of accidents, the truck continued to speed away, and was chased by police and later impounded.
"The truck was chased by a police officer at the picket and the cleaner of the truck was arrested while the driver managed to escape," Bharadwaj added.
A case has been registered under Sections 279 (rash driving or riding on a public way) and 304 (culpable homicide not amounting to murder) of the Indian Penal Code (IPC).