The incident took place last night when the deceased identified as Manoj shot himself dead with a country made pistol following a heated argument with the married woman, a senior police official said.
The body has been recovered and sent to Deen Dayal Upadhaya hospital for post mortem.
No suicide note has been found, police said.
Manoj, while living in Sagarpuri area came in contact with the married woman, aged around 30-35 years and mother of two daughters, a few month ago, according to police.
Later, he decided to live with the woman at her house in Vikaspuri as her husband was living in Himachal Pradesh.