The incident took place at around 3 pm, police said, adding that the woman's husband and their four children were present inside the house at the time of the incident.
The victim, identified as Aarti, sustained a bullet injury and is being treated at Guru Teg Bahadur Hospital. She is under observation currently, they said.
Police said the accused person was known to the victim's family. He visited them on Wednesday afternoon and opened fire at the woman following which she sustained a gunshot injury, a senior police officer said.
The accused fled the spot soon after firing a bullet at the woman, he said.
A case was registered and the matter is being probed, police said, adding the teams have been formed to trace the accused person.
(With inputs from agencies.)