The incident occurred when constable Ashok along with two other men went to a fish market in Mandawali area of east Delhi around 5.30 p.m.
Ashok, under the influence of alcohol, was reversing his car when Gopal and his grandmother were hit.
Both were rushed to a hospital where doctors declared the boy dead. His injured grandmother was recuperating.
Police said Ashok was off duty during the incident and was arrested.