Neeraj Gupta allegedly abducted the woman in his car on Friday in Viswakarma area here, they said.
The incident occurred when three girls booked a cab for returning home after a party. While waiting, they mistook another vehicle as their cab and boarded it, police said.
The man impersonating a cab driver stopped the car midway saying that a tyre has been punctured and asked the two women sitting at the back to shift to the front seat, police said.
As the two alighted, he drove away with the third woman and took her to an isolated place where he assaulted her, police commissioner Sanjay Agarwal said.