The man is helping police with their inquiries in relation to the attack, which took place between 2 am and 3 am on Monday morning.
Police say that the man was arrested at 8.45 pm last night, and they have asked for anyone who saw anything to get in touch with them.
The incident happened in the area of Elizabeth Street near Georgetown.
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.
Police officers investigating the attack issued a description of the suspect. They say he is around 5’10” tall, black, and that he was wearing a black jacket or blazer at the time.
Anyone who has any information at all is asked to contact the police on 612616 or the anonymous Crimestoppers line on 0800 555111.