The 51-year-old woman was attacked late Tuesday at knife-point by group of more than six men after losing her way heading to her hotel in a popular backpacker area of New Delhi, according to local media reports.
"She lost her way when this incident happened. Currently, the concerned police team has identified suspects and is interrogating them. The investigation is on," Delhi police spokesman Rajan Bhagat told AFP.
The woman, who cannot be named for legal reasons, told her friend about the attack when she eventually reached her hotel in Paharganj near the city's central Connaught Place, Bhagat said.
The woman said she had approached the group for directions near the New Delhi Railway Station after visiting a city museum, but they took her to a secluded spot and then raped her at knifepoint, the Press Trust of India news agency reported citing unnamed police sources.
The Danish embassy did not immediately respond to an AFP request for comment.
According to The Times of India newspaper, the woman had been in India for about a week, travelling first to Agra, the home of the Taj Mahal, before arriving in New Delhi on Tuesday.
The case comes weeks after a Polish woman claimed to have been drugged and raped by a taxi driver while travelling with her two-year-old daughter to New Delhi.
Last month India marked the first anniversary of the death of a student who was gang-raped on a moving Delhi bus in an attack that sent shockwaves across the nation.
The gang-rape triggered massive protests over the levels of violence against women, but in the last 12 months reported cases of local and foreign women being attacked have shot up significantly.
A judge last month sentenced three Nepalese men to 20 years in jail for the gang-rape of a US tourist in June in the northern state of Himachal Pradesh.
Six men were sentenced to life in prison last July for the gang-rape and robbery of a 39-year-old Swiss woman cyclist who had been holidaying in the central state of Madhya Pradesh.