Authorities in India have been preparing for the possibility her death could ignite more protests after riot police were deployed on the capital's streets in the wake of the attack amid simmering anger at the daily dangers women face.
The 23-year-old was airlifted to Singapore on Thursday after she was attacked by six men on a bus in New Delhi on December 16, raped, hit with an iron bar, and thrown from the vehicle.
Some Indian medics had criticised the decision to move her.
"We are very sad to report that the patient passed away peacefully at 4.45 am (2045 GMT) on 29 December 2012," Kelvin Loh, the chief executive of Singapore's Mount Elizabeth Hospital, said in a statement.
"Her family and officials from the High Commission of India were by her side."
The woman had remained in an extremely critical condition since being admitted to the hospital, Loh said, with doctors mounting a last-ditch battle overnight to save her life.
"Despite all efforts by a team of eight specialists in Mount Elizabeth Hospital to keep her stable, her condition continued to deteriorate over these two days," 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."
India's High Commissioner to Singapore T.C.A. Raghavan said the woman's family was "shattered" by her death.
"The scale of her injuries (was) very great," Raghavan told reporters at the hospital.
"It was very trying for the family. The girl of course was unconscious... I must say they (the family) bore the entire process with a great deal of fortitude and a great deal of courage."
He said arrangements were being made for the body to be returned to India in line with the family's wishes.
The decision to fly her out of the country by air ambulance was taken at a meeting of Prime Minister Manmohan Singh's cabinet on Wednesday and the government had promised to pay all her medical bills.
Home Minister Sushilkumar Shinde said the government's only concern was to ensure the victim received "the best treatment possible".
But Indian newspapers suggested the authorities, who have struggled to contain the nationwide protests over the attack, were keen to have her transferred out of the country.
An unnamed doctor who was part of a team of experts consulted about the transfer told The Hindu newspaper they had only been asked whether it was safe to move her and not whether it was the best course of action.
"The question was not whether there were any deficiencies in treatment that would be met by moving her... She was being given the best possible care," the doctor was quoted as saying.
Samiran Nundy, chairman of the organ transplant and gastro-surgery department of Delhi's Sir Ganga Ram Hospital, told the paper the transfer made little sense.
"I just can't understand why a critically ill patient with infection in blood and body, high grade fever and on the ventilator is being transferred," he said.
Singh has ordered an official inquiry into the gang-rape and new laws to protect women as well as stiffer penalties for the worst sex crimes.
And he said Delhi police would soon launch a drive to recruit more female officers as a confidence-building measure.
The government has also announced plans to post the photos, names and addresses of convicted rapists on official websites to publicly shame them. The campaign will begin in Delhi, which has been dubbed India's "rape capital".
India was rocked by a wave of protests in the week after the attack, prompting authorities to seal off large parts of the capital and to deploy riot police with water cannons and tear gas.
The Delhi gang-rape has shone the spotlight on a crime that occurs on a daily basis in India, with most such assaults taking place in rural areas.Police said on Friday that a 15-year-old schoolgirl had her throat slit after being gang-raped in the Pali Muqimpure area of Uttar Pradesh state. A hunt has been launched for three youths after the attack the previous day.