The accident took place around 5.45 AM in Kashmere Gate area in north Delhi.
The car had three occupants -- all Class XII students of Commerce stream of Delhi Public School, Mathura Road, said a senior police officer.
It has emerged during investigation that the driver had turned 18 last month and did not have a driving licence, said Deputy Commissioner of Police (North) Jatin Narwal, adding that he was driving the car of his friend's father.
If it emerges that he allowed the car to be driven by one without driving licence, he too would be booked, they said.
More From This Section
The injured, identified as Asif, Karan and Sanjay, were undergoing treatment at a hospital.
The deceased is yet to be identified.
They were sleeping on the footpath when the car, a hatchback, ran over them.
Two of the car's occupants who had fled from the spot after the accident later came to the Kashmere Gate police station and joined the probe.
However, they weren't wearing school uniforms, police said.
The driver has been sent for medical examination to determine whether he was drunk at the time of the accident and a report is awaited.
"Till now, the documents shown by the three students indicate that they are major but we are confirming from our end," the DCP said.