The 33-year-old woman had taken a taxi from the city of Mathura on Thursday when she was allegedly raped by the driver.
"She alleged the driver drugged her during the journey and she was assaulted after she lost consciousness," Delhi police spokesman Rajan Bhagat said.
The woman woke up on a bench outside a railway station in New Delhi on Friday, her daughter crying beside her. The driver apparently used some spray to render her unconscious and a medical examination had confirmed rape, Bhagat said.
Mathura police said they were searching for the driver. "The woman claims she was raped but there is no consistency in her statement. There are several contradictions in what she has stated," Mathura police official Gulab Singh told broadcaster CNN-IBN.
She was said to be a devotee of Hindu god Krishna living in Mathura for three years and exported garments, local reports said. The city located 135 kilometres from Delhi is believed to be the birthplace of Krishna.
Sexual violence has been a focus of public attention in India since the fatal gang rape of a student on a bus in New Delhi in December 2012.
Activists say little has changed in attitudes towards sexual assault, and attacks on women including foreign nationals continue unabated. A judge recently sentenced to life imprisonment a man accused of raping a Spanish woman in Mumbai. Earlier, six men were given life sentences in central India for the gang rape of a Swiss tourist.