The alleged crime took place in an apartment in Uppsala, a city about 50 miles north of the capital, Stockholm.
“This rape was broadcast live on a Facebook group and numerous people have been in touch regarding seeing this broadcast,” they said.
“The police went to said apartment, and in the apartment were three men and a woman. The three men were detained on the spot and then arrested by prosecutors at 2:30pm on Sunday.”
They said they were treating the case as one of aggravated rape.
Magnus Berggren, deputy chief prosecutor in Uppsala, told CNN the men remained in custody Tuesday and the investigation was continuing.
He said the Facebook group in question was a closed group “where you could post rather special things. Even for that group this was not anything normal.”
He confirmed Swedish media reports that the woman did not appear to be fully conscious.
“She was intoxicated. We’re not really sure how,” he said.
The police said the men arrested were born in 1992, 1996 and 1998 — meaning they are aged between around 19 and 25. The woman was born in 1986, making her around 31.
He appealed for anyone who has the video to send it to the police, and said prosecutors have been in touch with Facebook at their United States headquarters to request assistance.
“This is a hideous crime and we do not tolerate this kind of content on Facebook,” a Facebook spokesman told CNN in a statement. “We support local law enforcement who make data requests related to criminal investigations, particularly when it comes to the safety of young people. We respond to valid requests relating to criminal cases.”
CNN’s Sophie Morlin-Yron also contributed to this story.