Dated May 2, the letter highlights federal concern that Moore went to Cuba in March without approval, and asks for details about travel dates, people on the trip and reasons Moore might qualify for a journalist's licence to go to Cuba.
A spokesman for Moore declined to comment on what the film-maker was doing in Cuba, but said news reports about his taking victims of the September 11 attacks on New York's World Trade Centres there for health care were inaccurate.
In a response to the letter, Meghan O'Hara, the producer of the new film titled SiCKO, said the inquiry was politically motivated.
On Friday, Moore said he was the victim of a politically motivated investigation.
"I believe that the decision to conduct this investigation represents the latest example of the Bush administration abusing the federal government for raw, crass, political purposes," he wrote in a letter to Henry Paulson, treasury secretary, posted on his website (www.michaelmoore.com).
"There are a number of specific facts that have led me to conclude that politics could very well be driving this Bush administration investigation of me and my film."
Moore said he was surprised by the timing of the investigation.
He also claimed that the US health care and insurance industry - which are both targeted in the film - were supporters of Bush and the Republican Party.
"I demand that the Bush administration immediately end this investigation and spend its time and resources trying to support some of the real heroes of 9/11."
A treasury department spokeswoman declined to comment on any specific enforcement action against Moore.
Molly Millerwise, the treasury spokeswoman, said the agency "issues hundreds of letters each year asking for additional information when possible sanctions violations have occurred".
US restrictions on Americans travelling to Cuba are an extension of the 1962 US embargo against the communist country, and violating the rules can result in a prison sentence of up to 10 years or a $250,000 fine.
An Oscar winner for the 2002 anti-gun documentary Bowling for Columbine, Moore is well-known for works that attack corporations and politicians.
Released in an election year, Fahrenheit 9/11 took a searing view of Bush's actions after the September 11 attacks, as well as the US president's handling of the Iraq invasion.
The film proved to be Moore's biggest hit, earning $222m at box offices worldwide.
SiCKO, which premieres at this month's Cannes film festival in France, takes aim at the US pharmaceutical and health-care industry.
Ken Johnson, senior vice-president of the Pharmaceutical Research and Manufacturers of America, said in a statement that any review of America's health-care system should be "balanced, thoughtful and well-researched".
He said: "You won't get that from Michael Moore."