The couple was returning home after buying medicines for their ailing seven-months-old daughter.
The incident occurred on Sunday. The driver of the car sped away after the incident. The locals followed the car but could not stop it, they said.
However, since the number plate of the vehicle had come off after the accident, the driver was traced and arrested, a senior police official said.
It is suspected that the accused was driving the vehicle at a high speed at the time of the incident. However, no traces of alcohol were found, the official said.
On being hit by the car, the trio was thrown on a footpath. They sustained severe head injuries and were rushed to a nearby hospital. Mukesh died on the way to the hospital while his parents were referred to LNJP Hospital. They died while undergoing treatment, police said.
The eyewitnesses collected broken parts of the car, including the number plate, from the accident spot and handed those over to the police which led to the arrest of the car driver.