"The patient passed away peacefully at 4:45am on 29 Dec 2012," a statement from the hospital said. The patient's family had been by her side, it added.
She had been flown to Singapore for medical treatment on Thursday morning.
"The patient had remained in an extremely critical condition since admission to Mount Elizabeth Hospital," a statement from hospital chief executive Kelvin Loh said.
"She had suffered from severe organ failure following serious injuries to her body and brain. She was courageous in fighting for her life for so long against the odds but the trauma to her body was too severe for her to overcome," the statement went on.
"We are humbled by the privilege of being tasked to care for her in her final struggle," Mr Loh said.
A team of eight specialists had tried to keep the patient stable, but her condition continued to deteriorate over the two days she was at Mount Elizabeth Hospital, he added.
On Dec 16, the student, who has not been named so far, was raped by six men in a bus she and her male companion had boarded to go home after watching a movie.
The six men, who have since been arrested, beat and gang raped her and then stripped her before throwing her and her male companion, who was also beaten, out of the bus.
She was severely injured and underwent at least three operations.
The Indian Cabinet decided to fly her and her parents at government cost to Singapore based on the advice of a team of government and private doctors.
She was accompanied by her parents, two brothers and a team of Indian doctors led by Dr Yatin Gupta, head of the critical care unit at Delhi's Safdarjung hospital, where she was under treatment.
In Singapore, a multi-disciplinary team of specialists worked to treat her.
Mt Elizabeth said it did everything possible to stabilise her condition. Doctors fought for her life including putting her on maximum artificial ventilation support, optimal antibiotic doses as well as stimulants which maximised her body's capability to fight infections, the hospital said.
The brutality of the crime in the capital city triggered days of protests, resulting in violent clashes, with protesters demanding justice for the student and the police.