Sub-inspector Vijender Bishnoi later died at the All India Institute of Medical Sciences' Trauma Centre here, police said.
The SI went to meet Nikki Chauhan, 27, a resident of Uttam Nagar in west Delhi, around noon at a park in Dwarka's Sector 4 where the two had an argument. Vijender fired three shots at the woman before shooting himself, eyewitnesses told the police.
The woman was rushed to a nearby private hospital where she was declared brought dead. Vijender was rushed to the AIIMS where he succumbed to his injury in the evening.
According to informed sources, Nikki worked with a weekly newspaper and came in contact with Vijender when he was posted at the Uttam Nagar police station a few years ago.
The two allegedly had an affair but got married to different people.
According to police, Vijender, 30, was going through some personal problems and was absent from duty for the last 15 days. The department had issued him a notice for absence from duty without information, an official said.
A marital dispute case was pending against him in a Rajasthan court.
He rejoined duty on Saturday at the Ranhola police station in west Delhi and got a service weapon issued to him, police said.
The sources said the woman had been allegedly demanding money from Bishnoi, failing which she had threatened to lodge a rape complaint against him.