Duterte, given to incendiary language, was furious that the central bank's Anti-Money Laundering Council had failed to provide him an unspecified "assessment report".
"I'll count one to three and if you don't resign, I will treat you as a drug addict," said the 71-year-old, who is waging a brutal anti-drug campaign that has left more than 5,000 people dead since he became president in July.
In a speech after signing the 2017 national budget, he said: "Better prepare there because I'll give you a whack."
"You are all corrupt," he said, without naming any official.
"I am going to charge all of you there, criminally."
The four-member council is the state regulatory body enforcing the country's anti-money laundering law.
It is headed by central bank governor Amando Tetangco and also includes the government's chief insurance and securities regulators, as well as the council's executive director.
Duterte did not spell out what was in the report he was demanding.
The law prohibits the council from sharing any information with anyone else except under court order.
Duterte noted that Tetangco would be retiring soon. The governor completes his second six-year term in July next year.
Justice Secretary Vitaliano Aguirre later said Duterte was not referring to the central bank governor but "the office of the executive director, her deputy and the head of investigation".
In another speech to a women's group north of Manila, aired on television, Duterte accused the council's officials of failing to do their job and warned he would have the justice department file charges against them.
"I will personally arrest you," he said.
Duterte's spokesman did not reply to AFP's requests for clarification, while the council referred requests for comment to the central bank.
Aides told AFP the central bank's spokeswoman was unavailable for comment.
Last month Duterte had warned the central bank and the council to "avoid a confrontation between us".
At the time he said government agencies had to "do more, especially on digging records that would show laundered money".
The fiery Duterte won a landslide election victory this year after pledging to kill 100,000 criminals to prevent the Asian country from turning into a "narco-state".
Since July police said they have killed 2,124 drug suspects while more than 3,000 others were gunned down or stabbed by unidentified assassins.
Duterte asserts his anti-crime campaign was legal and has called US President Barack Obama a "son of a whore" and United Nations Secretary General Ban Ki-moon a "fool" for criticising it.
