All the students are from Kendriya Vidyalaya and aged between 8 to 13 years, police said. They sustained injuries on their legs, hands and heads.
Gungun, a Class IV student, suffered a brain injury and is admitted to Delhi's GTB Hospital, where her condition is stated to be critical, they said.
After the incident, the car driver fled from the spot.
The injured have been identified as Ritika and Gungun (Class IV), Anjali and Vishu (Class V), Krishan (Class VI) and Taru and Prashant (Class VII).
After the incident, all injured students were rushed to a nearby hospital, where some of them were discharged after first aid, while the remaining are being treated.
"We have booked a case against unknown person. A manhunt has been launched to nab him," the officer said.