It is the first time that a member of the ruling royal family will occupy this post.
Al-Falih, who chaired state oil giant Saudi Aramco until last week and had been Energy Minister since 2016, also lost his Industry and Mining Resources portfolios last week, Efe news quoted the decree as saying on Saturday.
The ministerial change comes as Riyadh prepares Aramco for an initial public offering (IPO).
In addition, the Saudi government appointed Osama al-Zamil as Deputy Minister of Energy, Industry and Mineral Resources for Industry Affairs, replacing Abdulaziz Al-Abdulkarim, according to the official Saudi Press Agency.
Prince Abdulaziz had earlier served as the Deputy Oil Minister from 1995 to 2005, after which he was named the Assistant Oil Minister until 2017.
He also serves as the State Minister for Energy Affairs.