The girl was shot in the head following a heated argument, the police said. She is a class 10 student at a Delhi school.
They were rushed to a nearby hospital after the incident.
The girl's condition was stated to be critical, while the boy was recuperating.
An FIR has been lodged against the class 11 boy following a complaint by the girl's uncle, Assistant Superintendent of Police Anoop Singh said.
The incident took place on Wednesday evening when they were returning home from a coaching centre on a scooty, police said.
(With inputs from PTI)