The 23-year-old medical student, who has not been identified, was taken to Singapore for specialist treatment but died from her injuries yesterday.
The incident has provoked protests and national debate about violence against women in India, with pressure on Prime Minister Manmohan Singh's government to get tougher on such crimes.
The outcry over the attack caught the government off-guard and it was slow to react. It took a week for Singh to make a statement, infuriating many protesters who saw it as a sign of a government insensitive to the plight of women.
In his statement, he said: "The need of the hour is a dispassionate debate and inquiry into the critical changes that are required in societal attitudes.
"I hope that the entire political class and civil society will set aside narrow sectional interests and agenda to help us all reach the end that we all desire – making India a demonstrably better and safer place for women to live in."
Hundreds of protesters took to the streets in the northern Indian city of Lucknow. In Hyderabad, in southern India, a group of women marched to demand severe punishment for the rapists.
Protests were also held in the cities of Chennai, Kolkata and Mumbai.
Authorities, worried about the reaction to the news of the woman's death, deployed thousands of policemen, closed 10 metro stations and banned vehicles from some main roads in the heart of New Delhi, where demonstrators have converged since the attack to demand improved women's rights.
The victim and a male friend were on a bus when six men beat them with metal rods and repeatedly raped the woman. Both were thrown from the bus.
Six men were arrested in connection with the rape and have now been charged with murder.
The attack and its aftermath have put gender issues centre stage in Indian politics. Issues such as rape, dowry-related deaths and female infanticide have rarely entered mainstream political discourse in the country.