A man in his 40s is accused of brutally raping the young woman, who is not a Swedish citizen. His son, aged 19, also faces allegations of rape and assault.
The pair, who were arrested earlier this week, were remanded in custody by Jönköping District Court on Friday afternoon.
Swedish rules allow suspects under a “lower degree of suspicion” to be held for up to a week, with room for the period to be extended further after that. They both deny the allegations.
The son's lawyer, Anders Tolke, said the son had recounted a different version of what had happened to what the girl had claimed.
“Yes, he has, but I cannot elaborate on what he has said,” he told the TT newswire after Friday's detention hearing.
Two other family members – a daughter and mother – also linked to the case, were both released earlier in the week pending investigation.
However, they remain under suspicion of keeping the girl locked up between September 2014 to March this year on locations in Jönköping, in southern Sweden, and Gothenburg on the west coast, Swedish Radio reported.
The teenager claims she was raped by the father and son on a number of occasions in the same period.
“It is a case reminiscent of human trafficking,” prosecutor Anna Mårtensson told Swedish Radio earlier on Friday.
The alleged victim's exact age is unknown, but she is believed to be under 18 and not related to the rest of the family.
According to the prosecutor she has said she is 17 years old.
The shocking allegations emerged on the same day as Norwegian police released images of a soundproof cellar built by a man charged with attempting to abduct Swedish and Norwegian children.
Police found no proof the cellar had been used, but at the time of the man's arrest he was thought to have travelled to addresses of at least 70 children he had tracked down on social media.
The two cases are not believed to be linked.