The outgoing minister, Prince Faisal who is also the king's son-in-law, requested he be relieved of the post, the report said.
Another of the king's sons, Prince Mutaib, is head of the Saudi Arabian National Guard, while his son Prince Abdulaziz is the deputy foreign minister and another son, Prince Turki, is deputy governor of the capital Riyadh.
But unlike in Western monarchies, the throne passes through brothers who are the sons of modern Saudi Arabia's founder, King Abdul-Aziz Al Saud.
Saudi Arabia is one of the world's last standing absolute monarchies and authority is concentrated within an aging and shrinking circle of Al Saud family leaders.