"The incident took place around 12.10 p.m. outside the Karkardooma Metro station in east Delhi. The woman, Deepti, and her father, 55-year-old Bishan Das, were shot from behind," a Central Industrial Security Force (CISF) official told IANS.
Deepti was taken to the Deepak Memorial Hospital where doctors declared her brought dead.
Bishan Das, who received two bullet injuries in his shoulder and stomach, was initially taken to Hedgewar Arogya Sansthan Hospital from where he was shifted to Guru Teg Bahadur Hospital where he is under treatment but stated to be out of danger.
The official added that the accused, identified as Pawan Kumar, 30, a resident of east Delhi's New Usmanpur area, is on the run. He fled the spot after the shooting, leaving his weapon and car outside the Metro station.
"Five empty cartridges and a double-barrel rifle have been recovered from the spot," the CISF official told IANS. The CISF looks after security at all Delhi Metro stations.
Das, a resident of Chirag Dilli in south Delhi, told police that there was discord between Deepti and her husband and a case was going on in court. He was returning along with his daughter from Karkardooma court after attending a hearing when they were attacked.
Meanwhile, a Delhi Metro official said the incident had not affected passenger services.
This was not the first shooting incident near any metro station, said a CISF official.
In February 2012, 42-year-old Shibu, a part-time driver, was shot at by an unidentified person near Gate no.2 of east Delhi's Mayur Vihar Phase-I Metro station.
In August 2011, a CISF trooper shot dead a female colleague at platform no.2 of east Delhi's Yamuna Bank metro station before killing himself.
This was the second shooting in the capital Tuesday. Bahujan Samaj Party leader and real estate tycoon, Deepak Bhardwaj, was shot dead in the morning at his south Delhi farmhouse.