The December 16 attack sparked a wave of protests across the country, with the unrest leaving a policeman dead and scores injured.
According to police and prosecutors, six men took turns to rape the woman and assault her with an iron bar, leaving her with intestinal injuries, before they threw her out of a bus that they had taken for a joy-ride.
The 23-year-old has already undergone three operations in India. She was airlifted from a hospital in New Delhi to the Mount Elizabeth Hospital overnight.
In a statement, the Mount Elizabeth Hospital described her condition in the intensive care unit as "extremely critical".
The Indian government, which is paying for the woman's treatment, approved the decision to transfer her from Delhi's Safdarjung Hospital where she had been treated since the December 16 assault on a bus in the centre of the capital.
Visa arrangements were also fast-tracked to enable the victim's relatives to keep watch over her in Singapore.
"The hospital and the family have requested that the privacy of the patient and the family be respected," a statement from the high commission said.
While doctors in Singapore did not give details about the treatment she has received since her early morning arrival, their counterparts at Safdarjung said Mount Elizabeth had been chosen as it has a multi-organ transplant facility.
"The said hospital has a state-of-art multi-organ transplant facility," B D Athani, medical superintendent of Safdarjung Hospital in Delhi, said.
"The arrangement has also been made for the family to accompany her as the treatment may take [a] longer period.
"She has had to be operated upon three times. With fortitude and courage she has survived the after-effects of the injuries so far but her condition continues to be critical."
The gang-rape has prompted widespread street protests in India, not only in revulsion at the savage nature of the attack but also because it tapped into simmering anger at the level of violence against women.
Official figures show that 228,650 of the total 256,329 violent crimes recorded last year were against women, with the number of rapes in the capital rising 17 per cent to 661 this year.
Gang-rapes are reported on a daily basis, with police revealing on Thursday that a 42-year-old woman had been found overnight dumped on a road in south-east Delhi after she was gagged, sedated and then raped by three men.
Prime minister Manmohan Singh told a gathering of chief ministers from across India on Thursday that there was a "problem" which "requires greater attention" by the central and state governments.
He promised to review laws on women's safety.
Six men are in custody in connection with the assault.
Mr Singh, whose government has been stung by criticism about the notoriously slow Indian justice system, said their case would be dealt with swiftly.
"The culprits have been apprehended and the law will deal with them expeditiously," he said.
The government has already set up a commission of inquiry into the attack while a separate panel has been asked to suggest changes in the laws to make punishment for such horrific crimes stiffer.
"Laws regarding the safety of women will be reviewed," Mr Singh said.
India was rocked by a wave of protests in the week after the attack, prompting authorities in Delhi to seal off large parts of the capital.
With most of the roadblocks having now been lifted, activists are planning to hold fresh protests at the India Gate monument where some of the largest demonstrations have taken place.