Police said the man, 20, was arrested last night in the coastal town, which lies close to the border with Norway. He is likely to be remanded in custody during the day.
Police say the woman was 40 and lived in Stockholm. Her family has been informed of her death. According to Expressen she had spent the evening at the popular nightclub The Cod, where she had apparently bought drinks just before 3am on Sunday. Several witnesses had seen her at the bar.
Her body was found in an alley between a restaurant and a fish storage warehouse
The investigation is continuing at the scene, which is in the middle of a popular tourist area lined with restaurants.
The man suspected of her killing lives in the Gothenburg area, and was not previously known to police.
No motive for the murder has yet been identified, and police are so far unsure as to the sequence of events on the night of the killing. They are now searching for witnesses who were in the Torskholmen area at around 3am on Sunday morning.