The 34-year-old man was arrested at 8.45 pm on Monday night over the attack, which occurred in the early hours of Monday morning.
He has been released on police bail until next Tuesday.
The incident happened in the area of Elizabeth Street near Georgetown between 2 and 3 am on Monday morning.
The woman, who was walking home after being out with friends, was talking to the man in the Co-op carpark, before the attack nearby.
The victim is receiving support from specially-trained police and partnership agencies.
Anyone who has any information at all is asked to contact the police on 612616 or the anonymous Crimestoppers line on 0800 555111.