According to The Wall Street Journal, both members of the royal family were detained on Friday by royal court guards, who were wearing masks and dressed in black.
The guards also detained one of the brothers of Mohammed bin Nayef bin Abdulaziz al Saud.
Further details of the detentions remain unknown.
Mohammed bin Nayef bin Abdulaziz al Saud was crown prince from 2015 to 2017, but King Salman changed his successor in 2017, naming Mohammad bin Salman bin Abdulaziz al Saud the new crown prince.