Sam Bankman-Fried was arrested at the request of the US, Bahamas Attorney General Ryan Pinder says.
FTX founder faces sealed indictment by US Attorney for Southern District of New York.
SEC has authorized charges relating to alleged violations of its securities laws.
FTX's demise marked the latest turmoil for the cryptocurrency industry this year.
Users pulled $6 billion (€5.7 billion) from the platform in three days.
FTX's chief executive Thomas Bankman-Fried acknowledged risk management failures but said he did not commit fraud.