A hospital source said Archana Gupta succumbed to injuries on Thursday.
A pistol and a rifle were seized from the car in which Raju Singh fled from the spot after the incident, Special Commissioner of Police, Law and Order (south), R P Upadhyay said.
"We have arrested Raju Singh and Hari Singh in connection with the incident. They will be produced in a city court later in the day. Police will seek their remand for seven days," he said.
Upadhyay said the woman who was injured during the incident succumbed to injuries.
On Wednesday, they were detained in Uttar Pradesh's Gorakhpur city.
Police had earlier seized two rifles and 800 bullets from Raju Singh's farm house in south Delhi's Vasant Kunj area.
In his complaint to police, Archana Gupta's husband had said that they were at the farm house on Monday night to celebrate the New Year along with friends and around midnight, two-three rounds were fired by Raju Singh.
Immediately, he noticed that his wife had fallen down and was bleeding.
The Delhi Police was informed and a medicolegal case was registered, a hospital spokesperson said.
Raju Singh was booked under relevant sections of the Indian Penal Code and the Arms Act, police said, adding that he has five other cases registered against him.
His wife is a former member of the legislative council from Bihar, they said.
The farm house is owned by Singh's mother where he lives with his family. Singh's two brothers also live with their families in the farm house, police added.