The suspension of the Economic and Financial Crimes Commission (EFCC) chairman AbdulRasheed Bawa was the second dismissal of a top official by Tinubu since he came to office two weeks ago promising economic reforms.
"Mr Bawa has been directed to immediately handover the affairs of his office to the Director, Operations in the Commission, who will oversee the affairs of the Office of the Chairman of the Commission pending the conclusion of the investigation," the government statement said late Wednesday.
It said the suspension followed "weighty allegations of abuse of office levelled against him."
The presidency statement did not give more details about the allegations against the EFCC chairman.
The Department of State Services (DSS) domestic security and intelligence agency later said it questioned Bawa.
"Bawa arrived a few hours ago. The invitation relates to come investigative activities concerning him," it said.
The EFCC investigates money-laundering, graft and other financial crimes such as internet scams.
Bawa's suspension follows the ousting and arrest of Nigeria's central bank chief Godwin Emefiele, who was detained by the domestic security services last week as part of a probe into his role.
Tinubu's predecessor Muhammadu Buhari made anti-graft a major part of his campaigns for election in 2015 and re-election in 2019, but Nigeria remains one of the lowest ranked on Transparency International's widely watched corruption perception index.
Tinubu, who came to power at the end of last month following a highly contested February presidential election, promised reforms to help Africa's largest economy and one of the continent's top oil producers.
The struggling economy is one of a host of issues facing Nigeria's new leader, including a security crisis with the armed forces battling jihadists, heavily armed criminal gangs and separatist militants in different parts of the country.