"She is a French national. A case of murder has been registered," New Delhi police spokesman Rajan Bhagat told the AFP wire service. "We're looking for the suspects.”
He said he could not immediately release the woman's identity or comment on media reports that the victim had been strangled.
The woman was aged between 25 and 35, according to media reports.
Her body was found in a “highly decomposed state” in the Hindustan guest house in Paharganj, an area popular with backpackers for its cheap hotels and restaurants.
The room she was found in had been booked by a handicraft shop owner who told a friend that a foreigner had died in his room, The Hindu newspaper quotes police as saying.
She had booked into another hotel in the same area on 30 March and her visa would have run out on 10 April, it reported.
The trader has since disappeared.
New Delhi is widely perceived as an unsafe city for women with official data showing that among the 35 biggest cities in the country, it has the largest numbers of crime cases against women.