A 28-year-old woman died in Delhi's Vishwas Nagar area in Shahdara, police said on Wednesday, adding her body bore bullet injuries.
The woman was identified as Shivangi Kasana, a teacher at a private school in Delhi, they said.
Police said they were informed about the death by hospital authorities around 11 am on Wednesday.
The woman got married a year-and-a-half ago and had a daughter.
The woman's husband, Prashant Kasana, claimed that she shot herself with a pistol and that he was present at home when the incident took place, a senior police officer said.
However, no suicide note has been found from the spot, he said.
The woman was admitted in a nearby hospital where she was declared dead. She sustained a bullet injury on her head, he added.
A Sub-Divisional Magistrate has been informed and the statement has been recorded, the officer said.
On the basis of enquiry and inspection of site, a case has been registered in connection with the incident, the officer added.
The weapon involved in the incident has been seized and the husband has been arrested, the police said.
Police said they are probing all angles including that of any family dispute.
The exact cause of death will be established after the postmortem, police said.