The incident happened on Saturday in the Bhajanpura area of the national capital, according to police.
The girl shot at the 50-year-old woman with a pistol around 5.30 pm, they said.
The injured woman, whose son allegedly raped the girl, runs a grocery shop.
She was rushed to GTB Hospital, police said.
Both the girl and the accused are minors, and, hence, their identities were not revealed.