The incident took place on Saturday, following which the man was arrested, they said.
They were in a relationship but the woman ended it. He attacked the victim at her relative's house, police said.
The condition of the woman, who is a chartered accountant, is stable.
The accused, who works with a jagran mandal, had been harassing the woman, they said.
On Saturday, when he learnt that the woman was at her relative's house, he went there, and shot at her as soon as she opened the door, police said.
Hearing the gunshots, the victim's relatives rushed to the spot and took her to a hospital, they said.
The man was arrested from Shahdara, police said.