Marius Borg Hoiby is the stepson of the heir to the Norwegian throne, Crown Prince Haakon, and the son of Mette-Marit from a previous relationship.
He has no royal title or official duties.
Borg Hoiby was arrested late on Monday in Oslo on a preliminary charge of having had "sexual intercourse with someone who is unconscious or for other reasons unable to resist the act".
A preliminary charge comes before a formal charge and allows authorities to detain suspects during an investigation.
Police did not say when the alleged rape occurred, but only that "the victim must have been unable to resist the act".
Norwegian media said Borg Hoiby denied the accusation.
Hege Salomon, the lawyer for the woman who was allegedly raped, said "she is having a hard time".
She told Norwegian broadcaster NRK that police, not the woman, had brought the case. The woman was not identified.
The royal palace had no comment, the news agency NTB said.
On August 4, police officers responded to a disturbance in downtown Oslo and briefly detained Borg Hoiby.
He faced preliminary charges of bodily harm and criminal damage and was released.
Details were unclear but police said there was "a relationship between the suspect and the victim".
More preliminary charges have since been filed against Borg Hoiby, including violating several restraining orders and driving without a valid driver's licence.
In all, the cases involve four women and one man.
The case was top news in Norway, where the royals are popular.
Borg Hoiby, 27, lives with the royal couple and their two children, Princess Ingrid Alexandra and Prince Sverre Magnus.
Norway's future queen made headlines in 2001 when she married Haakon because she was a single mother who had lived a freewheeling life with a companion who had been convicted on drug charges.
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