The 51-year-old tourist was attacked by a group of men in the Paharganj area on Tuesday evening. Police say she was robbed and raped at knife point.
The woman flew out of India on Wednesday morning, reports say.
Scrutiny of sexual violence in India has grown since the 2012 gang rape and murder of a student on a Delhi bus.
The government tightened laws on sexual violence last year after widespread protests following the attack.
The Danish woman told police that she approached the group of men after losing her way back to her hotel near New Delhi Railway Station.
The men robbed her of her belongings and raped her, police spokesperson Rajan Bhagat told the BBC.
“She reached her hotel and reported the incident to the manager who called in the police and the investigation is now under way,” Mr Bhagat said. No arrests have been made yet.
Paharganj, a busy backpacker district frequented by foreign tourists, is located in the heart of Delhi, not far from Connaught Place.
Last March a Swiss tourist was gang raped and her partner attacked by a group of men in Madhya Pradesh state. Six men were jailed for life for the attack in July.