In a statement, police said the rape “concerns [a] sexual act without intercourse” and that the victim was “said to have been unable to resist the act”.
According to local reports, the Norwegian palace has declined to comment on the latest arrest of Mr Høiby.
Mr Høiby was arrested by police at 23:12 (22:12 GMT) on Monday in a car with a victim from a separate incident.
In relation to this separate incident, on 4 August, he faces charges of violence and criminal damage.
Police said, external on Tuesday that the charges had been expanded to include “maltreatment” in close relationships and “another violation” of a restraining order against the same victim.
They added that a report had been made for driving without a valid driver’s licence.
Mr Høiby’s residence at Skaugum, close to where the crown prince and his wife live, has also been searched by police.
Mr Høiby has also previously been charged with abuse against ex-girlfriends Julianne Snekkestad and Nora Haukland, as well as with threatening a man.
