The detentions came hours after the new committee, headed by Crown Prince Mohammed bin Salman, was formed by royal decree.
Those detained were not named.
BBC security correspondent Frank Gardner says Prince Mohammed is moving to consolidate his growing power while spearheading a reform programme.
It is not clear what those detained are suspected of. However, Saudi broadcaster Al-Arabiya said fresh investigations had been launched into the 2009 Jeddah floods and the outbreak of the Mers virus which emerged in Saudi Arabia in 2012.
The new anti-corruption committee has the power to issue arrest warrants and travel bans, the state-owned Saudi Press Agency (SPA) reported.
Separately, the heads of the Saudi National Guard and the navy were replaced in a series of high-profile sackings.
SPA said King Salman had dismissed National Guard minister Prince Miteb bin Abdullah and navy commander Admiral Abdullah bin Sultan bin Mohammed Al-Sultan.
No official explanation was given for their removal.
Prince Miteb, son of the late King Abdullah, was once seen as a contender for the throne and was the last member of Abdullah’s branch of the family at the highest echelons of Saudi government.
Our correspondent says Prince Mohammed, who already serves as defence minister, now has nominal control over all the country’s security forces.
Prince Mohammed recently said the return of “moderate Islam” was key to his plans to modernise Saudi Arabia.
Addressing an economic conference in Riyadh, he vowed to “eradicate the remnants of extremism very soon”.
Last year, Prince Mohammed unveiled a wide-ranging plan to bring social and economic change to the oil-dependent kingdom. (Courtesy BBC)