Saudi authorities on Saturday carried out a new wave of arrests, targeting royals and cabinet ministers in a crackdown against alleged corruption that comes as the Saudi leadership is seeking to consolidate power during a period of political transition.

Billionaire Prince al-Waleed bin Talal, a prominent member of Saudi Arabia’s royal family and one of the world’s wealthiest men, was among at least 10 princes and more than two dozen current and former ministers detained by Saudi authorities on Saturday night, according to people familiar with the matter.

Mr. al-Waleed is a top investor in Apple Inc. and Twitter Inc. He faces charges of money laundering, according to a person familiar with the matter.

The targeting of senior princes like Mr. al-Waleed and of sitting cabinet ministers represents an escalation of a campaign of arrests launched by the Saudi leadership in recent months. Crown Prince Mohammed bin Salman—elevated to heir apparent after his predecessor was deposed this summer—is consolidating power before his octogenarian father, King Salman, is expected to abdicate either later this year or early next year, people familiar with the matter said.

Mr. al-Waleed has long been one of Saudi Arabia’s most prominent business voices, but he hadn’t been seen as a major player in domestic politics. His father, Talal bin Abdulaziz al Saud, however, has previously opposed Prince Mohammed’s rise to power.