Bin Nayef was reportedly summoned to the Safa Palace on the evening of June 20 for what he thought was a regular meeting with King Salman bin Abdulaziz.
Instead, he was reportedly taken into a side room and stripped of his mobile phone by royal officials, who told him he needed to give up his role as crown prince and relinquish the powerful role of Interior Minister.
Bin Nayaf initially refused, according to the newspaper, but as the night dragged on towards sunrise he eventually gave in.
In 2009, Bin Nayef narrowly survived an al-Qaeda assassination attempt.
It has been rumoured that he began taking painkillers after the attack, and became addicted. Bin Nayef has not commented publicly on these claims, which could not be independently verified.
Bin Nayef was also reportedly opposed to the Saudi-led diplomatic campaign against its neighbour, Qatar, which may have hastened his demotion.
Saudi and its three allies said yesterday that they were no longer insisting Qatar meet a list of 13 demands, including closing al-Jazeera, the television network.