He is scheduled to appear on Tuesday in a magistrates court in the Caribbean country’s capital, Nassau.
Police said Mr Bankman-Fried was arrested for “financial offences” against laws in the US and The Bahamas.
Last month FTX filed for bankruptcy in the US, leaving many users unable to withdraw their funds.
According to a court filing last month, FTX owed its 50 largest creditors almost $3.1bn (£2.5bn).
It is unclear how much people who have funds in the exchange will get back at the end of bankruptcy proceedings – though many experts have warned it may be a small fraction of what they deposited.
The FTX exchange allowed customers to trade normal money for cryptocurrencies like Bitcoin.
Mr Bankman-Fried was once viewed as a young version of legendary US investor Warren Buffett, and as recently as late October had a net worth estimated at more than $15bn.
He had become well known in Washington DC as a political donor, mostly to Democrat politicians or groups, supposedly supporting pandemic prevention and improved crypto regulation.
The fall of ‘King of Crypto’ Sam Bankman-Fried
Crypto giant FTX collapses into bankruptcy
Mr Bankman-Fried will be held in custody “pursuant of our nation’s Extradition Act,” the Attorney General of the Bahamas said in a statement.
“Earlier this evening, Bahamian authorities arrested Samuel Bankman-Fried at the request of the US Government, based on a sealed indictment filed by the SDNY [Southern District of New York]. We expect to move to unseal the indictment in the morning and will have more to say at that time,” the US Attorney’s office in Manhattan said in a tweet.
Wall Street regulators also said that they would be taking action against Mr Bankman-Fried.
“We commend our law enforcement partners for working to secure the arrest of Mr Sam Bankman-Fried in the Bahamas on federal criminal charges,” US Securities and Exchange Commission (SEC) official Gurbir Grewal said in a statement.
“The Securities and Exchange Commission has separately authorised charges relating to Mr. Bankman-Fried’s violations of our securities laws, which will be filed publicly tomorrow in the Southern District of New York,” he added.
Mr Bankman-Fried had been due to testify about the collapse of FTX before the US Congress on Tuesday.
However, he will now be unable to testify, according to Congresswoman Maxine Waters, who said in a statement that she was surprised to hear that he had been arrested.
Mr Bankman-Fried’s lawyer did not immediately reply to a BBC request for comment.
FTX, the owner and operator of the FTX.COM cryptocurrency exchange, was founded in 2019 by Mr Bankman-Fried, a former Wall Street trader and ex-Google employee Gary Wang.
It became the second largest crypto exchange in the world, trading about $10bn of cryptocurrencies a day.
But on 11 November FTX filed for bankruptcy protection after users pulled $6bn from the platform in three days and rival exchange Binance abandoned a rescue deal. At the same time, Mr Bankman-Fried resigned as FTX’s chief executive.
In a series of interviews and public appearances in recent weeks, Mr Bankman-Fried has acknowledged that mistakes were made at the firm, but sought to distance himself from accusations of illegal activity.
“I didn’t ever try to commit fraud,” he said at the New York Times’ DealBook Summit at the end of last month.
The collapse of FTX came during a tumultuous year for the cryptocurrency industry. This year Bitcoin has lost more than 60% of its value, while other cryptocurrencies have also slumped.
Source: The BBC