An American Free Speech Test?
Sicko, in which the director attacks the US health system, has had its first screening at the French film festival.
But the US Treasury is investigating whether Moore broke the trade embargo against Cuba by filming there.
Moore told reporters he had to send a copy of the film to an unnamed country in case they confiscated the original.
The Treasury said it had no record of a licence being issued authorising travel to Cuba, and Moore could face a fine or jail.
A copy of Sicko was sent out of the US less than 24 hours after he was told about the investigation, the film-maker said.
The documentary includes sequences in which Moore takes rescue workers from the 11 September attacks in New York to near the US naval base at Guantanamo Bay and a Cuban hospital.
The group are suffering from conditions thought to be linked to their work clearing up debris from the site of the World Trade Center.
"The point was not to go to Cuba, it was to go to American soil, to Guantanamo Bay, to take the 9/11 rescue workers there to receive the same healthcare that they are giving the al-Qaeda detainees," Moore said.
"No film-maker should ever have to be talking about jail or fines or where he or she can travel."
"This office has no record that a specific licence was issued authorising you to engage in travel-related transactions involving Cuba," it said.
Moore told a Cannes press conference: "I know a lot of you have written: 'How dumb are they to give us all this publicity?'
"But I am the one who is personally being investigated, and I am the one who is personally liable for potential fines or jail so I don't take it lightly."
The film-maker described Sicko as a "call to action" over the provision of healthcare.
"We are never going to have real change in the United States if the public doesn't see that it will only happen when they rise up out of their theatre seats and do something about it."
Moore's film looks at healthcare provision in the UK, France and Canada, and the director said the US should adopt the best elements of other countries' systems.
"What we should do as Americans is what we always do... just take all the things that each of you are doing right and put it into one system, and call it the American system."
The film-maker won the Palme d'Or in Cannes in 2004 with Fahrenheit 9/11, an examination of the White House's decision to go to war in Afghanistan and Iraq.He won an Oscar in 2002 for the documentary Bowling for Columbine, a critique of US gun culture in the wake of the shootings at Columbine High School.