Her condition deteriorated over the past two days, the hospital said on Saturday.
"She had suffered from severe organ failure following serious injuries to her body and brain" the Straits Times quoted the hospital's chief executive Kelvin Loh as saying.
"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."
He added: "We are humbled by the privilege of being tasked to care for her in her final struggle.
"We acknowledge the faith the Indian government and the patient's family placed with us to ensure the best care possible was indeed provided to her at Mount Elizabeth Hospital.
"We share their huge sadness at her passing and will work with the high commission of India to provide the family support in this time of grief."
He said the woman had remained in an extremely critical condition since admission to the hospital.
The woman had suffered multiple-organ failure after she was raped by six men in a moving bus in Delhi on December 16 and dumped on a roadside.