The girl, studying at a school in Delhi, was shot at in the head by the boy following a heated argument, they said.
The incident took place last evening near Vartalok society in Vasundhara when the duo was returning home on a scooty from a coaching centre, police said.
The boy also shot at himself with the licenced pistol, belonging to his father, they said.
They were rushed to a nearby hospital, police said, adding that the girl's condition was stated to be critical, while the boy was recapturing.
Police have recovered the pistol from the spot and have summoned the boy's father for questioning.