Both princes had served previously in the post of interior minister, overseeing security and surveillance inside the kingdom
Another source said the princes were accused of "treason".
The New York Times also reported the detentions, adding that Prince Nayef's younger brother Prince Nawaf bin Nayef had also been detained
"I think absurd is exactly the right word," Saudi Arabia's Foreign Minister Prince Faisal bin Farhan Al Saud
Saudi Arabia is pulling out all the stops to ensure the success of Aramco's initial public offering after Crown Prince Mohammed bin Salman finally decided to offer shares
The three-day forum is hosting financiers, governments and industry leaders who would discuss global trade and explore the trends, opportunities and challenges shaping the global investment landscape
The crown prince has become a pariah in Washington since Khashoggi's killing at the hand of Saudi agents in the kingdom's Istanbul consulate
In the wide ranging interview with the Saudi-owned newspaper, the crown prince also commented on recent attacks on oil tankers near the Strait of Hormuz and Saudi Arabia's 2030 development goals
The Crown Prince arrived on a less than 30-hr visit, a day after concluding his tour of Pakistan where he said dialogue was the only way to resolve "outstanding issues" between India and Pakistan
The Crown Prince, who is on his first state visit to India, will hold delegation-level meetings with Prime Minister Narendra Modi on Wednesday
According to the citation, the Crown Prince provided "outstanding support for reinvigorating Pak-Saudi bilateral relationship"
The trip comes days after a suicide bomber killed 44 Indian paramilitary police in the disputed Kashmir region
The purge of top business elites comes as Saudi Arabia is struggling to get a grip on the proxy war with Iran in neighboring Yemen
Prince Mohammed has been the main driver of the once-staid kingdom's more aggressive regional push since he took over as defence minister in early 2015
The 2015 purchase appears to be one of several extravagant acquisitions - including a $500 mn yacht and a $450 mn Leonardo da Vinci painting - by a prince who is leading a sweeping crackdown in Saudi
The new crown prince has embarked on a course that will have massive repercussions in West Asia and beyond
The remarks seemed aimed at religious ultra-conservatives who have been tolerated by the ruling Al Saud family in exchange for their support