The incident is believed to have occurred at about 4.50am in the Duke Street area of Sheffield after the woman is thought to have gotten into a taxi.
Temp Det Insp Graham Stead, said: “We believe the woman got into a taxi from the city centre, close to West Street, and was taken to the Duke Street area, where the offence is said to have occurred in the car. An investigation is now underway and we have a dedicated team of officers working on this.
“This is being treated as an absolute priority and we are already pursuing a number of strong lines of enquiry. A thorough review of CCTV footage of the area, including the route we believe the taxi took, is also now underway.
“The woman is being supported by specialist officers and I’d urge anyone who has any information about what happened to contact us.”
Anyone with information can pass it to police by calling 101 and quoting incident number 235 of 23 October 2016.”
Information can also be given to Crimestoppers anonymously on 0800 555111.