Separately, the head of the Saudi National Guard, once a leading contender to the throne, as well as the navy chief and the economy minister were replaced in a series of high-profile sackings that sent shock waves in the kingdom.
The crackdown was reported immediately after a new anti-corruption commission, headed by powerful Crown Prince Mohammed bin Salman, was established by royal decree late Saturday.
Saudi-owned Al Arabiya television reported that the princes, four current and dozens of former ministers were arrested as the commission launched a probe into old cases such as floods that devastated the Red Sea city of Jeddah in 2009.
State-run Saudi Press Agency said the commission's goal was to "preserve public money, punish corrupt people and those who exploit their positions".
Saudi billionaire Prince Al-Waleed bin Talal was among those arrested, Saudi news websites said though there was no official confirmation. The prince was not reachable for comment.
An aviation source told AFP that security forces had grounded private jets in Jeddah, possibly to prevent any high-profile figures from leaving.
Meanwhile, the kingdom's top council of clerics tweeted that anti-corruption efforts were "as important as the fight against terrorism", essentially giving religious backing to the crackdown.
"The breadth and scale of the arrests appears to be unprecedented in modern Saudi history," said Kristian Ulrichsen, a fellow at the Baker Institute for Public Policy at Rice University.
"The reported detention of Prince Al-Waleed bin Talal, if true, would send shock waves through the domestic and international business community," Ulrichsen told AFP.
- Widening crackdown -
The purge comes less than two weeks after Prince Mohammed welcomed thousands of global business titans to Riyadh for an investment summit, showcasing his economic reform drive for a post-oil era.
It follows a wave of arrests of influential clerics and activists in September as the 32-year-old prince, often known as MBS, cements his grip on power.
Analysts said many of those detained were resistant to Prince Mohammed's aggressive foreign policy that includes the boycott of Gulf neighbour Qatar as well as some of his bold policy reforms, including privatising state assets and cutting subsidies.
The latest purge saw Prince Miteb bin Abdullah sacked as the head of the National Guard, an elite internal security force. His removal consolidates MBS's control of the kingdom's security institutions.
To analysts, MBS's meteoric rise has seemed almost Shakespearean in its aggression and calculation. In June, he edged out a 58-year-old cousin, Prince Mohammed bin Nayef, to become heir to the throne.
At the time, Saudi television channels showed the bearded MBS kissing the hand of the older prince and kneeling before him in a show of reverence. Western media reports later said that the deposed prince had been placed under house arrest, a claim strongly denied by Saudi authorities.
Already viewed as the de facto ruler controlling all the major levers of government, from defence to the economy, the prince is widely seen to be stamping out traces of internal dissent before a formal transfer of power from his 81-year-old father King Salman.
At the same time, he has projected himself as a liberal reformer in the ultra-conservative kingdom with a series of bold moves including the decision allowing women to drive from next June.
Foreign diplomats predict MBS, set to be the first millennial to occupy the Saudi throne, could well be in control of Saudi Arabia for at least half a century.