According to the girl's testimony she met the four Swedish teenagers in a bar on Saturday night.
The teenager told police that they had left the bar together after they had been drinking and returned to the hotel where the Swedes were staying.
According to Turkish media reports the hotel receptionist refused to allow the group to enter and they instead headed to the beach for a swim. When they later returned to the Swedes' hotel all five managed to sneak in.
In her police report the girl has said that by that time she was tired and all she wanted to do was sleep. But according to Turkish media reports the men then proceeded to rape her until the morning.
The teenager reported the alleged rape on Sunday morning.
The men, three of whom were aged 18 and one 19, were arrested by Turkish police on the street in Alanya later on Sunday.
According to Turkish police the four "took turns" to rape the woman.
The four meanwhile deny raping the 19-year-old and according to Swedish media reports the men were released by Turkish police after questioning on Monday evening.
The Norwegian foreign ministry has confirmed that it has been informed about the case.