Radhika Tanwar (21) was attacked by an unidentified man near a foot-over-bridge outside Ramlal Anand College in Dhaula Kuan's Shantiniketan area at around 10:20 am, a senior official said. The victim resided in Naraina Village.
The incident has caused outrage in the city, which was celebrating International Women's Day, and again raised questions over the law and order situation in the capital.
Angry over the murder, a large number of students in Delhi University south campus staged a protest demonstration against the lack of security for students and blocked the Ring Road. Some locals also joined the protest.
"A man came from behind and opened fire at her. A bullet hit her stomach. The attacker managed to flee the scene soon after the incident," a senior police official said.
Passersby took the girl in an autorickshaw to Safdurjung hospital where she was declared brought dead, the official said.
The incident evoked strong reactions from MPs, including RJD leader Lalu Prasad Yadav, who condemned the incident.
Congress MP from West Delhi Mahabal Mishra pointed fingers at the Union Home Ministry saying it was directly responsible for the incident as Delhi Police, which has to ensure safety of the people of the city, comes under it.
NCW Chairperson Girija Vyas and CPI(M) Politburo member Brinda Karat termed the incident as "very sad" and wondered why such incidents were recurring. "I condemn the incident. Why such incidents are recurring?" Vyas said.
Karat said, "it is a very sad incident. The incident took place when we are talking about women empowerment and celebrating the Women's Day."
The motive behind the incident is being investigated, the police official said, adding that they suspect the hand of a "stalker" in the murder.
"We are investigating all angles. It could be a case of a stalker committing the murder. But we cannot say anything now as the investigations are at the initial stages," the official said.
The girl's family said she left home for college at around 9 am. "She never told us that she was facing problems from somebody. We don't know anything and we don't suspect anybody as of now," Vipin, girl's brother, said.
Radhika's father Rajender Singh said "I have no clue what's happening. I don't know who could have done this to my daughter. She had no enmity with anyone."
H G S Dhaliwal, Deputy Commissioner of Police (South), said, "it appears that the girl was specifically targeted with an intention to kill her. There was no attempt to snatch her money or purse."
The attacker appeared to be known to the victim and was trailing her, he said.
Around 25 per cent of the murder victims in the national capital are women. Last year, 519 murders were reported in the capital while the figure was 527 for 2009, 528 (2008) and 467 (2007 and 2006), the police official said.
According to the latest National Crime Records Bureau report, Delhi has earned the dubious distinction of being the most unsafe metro, topping the list of ignominy in number of atrocities against women.
This year so far, 42 women were raped and 73 molested in the capital. In January, 17 cases of rape were reported besides 29 molestation cases with police claiming that they have solved 95 per cent of rape cases and 83 per cent of molestation cases.
In 2010, the city witnessed 489 rape incidents as against 2009's 459. The figures for 2006 was 609 followed by a drop to 581 next year while in 2008 it further dipped to 466.
Almost similar was the case with molestation cases in the capital in these years but it showed an increase this year to 585 from last year's 532. While 2008 had 597 cases, there were 835 incidents in 2007 wand 713 in 609.