Disney CEO Bob Iger told ABC employees about the demand at a town hall meeting on Monday, The Hollywood Reporter said.
He did not name the film, but Deadline reports that it is Pirates of the Caribbean: Dead Men Tell No Tales.
Mr Iger said Disney is refusing to pay, and that the studio is working with federal investigators.
He added that the hackers had demanded the ransom in bitcoin and that they would release the film online in a series of 20-minute chunks unless it was paid.
It is not the first film studio to be threatened with online leaks.
Last month, a group of hackers uploaded the fifth season of Orange is the New Black after Netflix refused to pay a ransom.
Dead Men Tell No Tales is the fifth instalment of the Pirates franchise and will see Johnny Depp's Captain Jack Sparrow return to the ocean alongside Geoffrey Rush and Orlando Bloom.
It is due to be released in cinemas in the US on 26 May.
Mark James, security specialist at IT security company ESET, said: "Anything that has a value will always be a potential victim of theft, either digital or physical. If someone has it and someone wants it then in theory there's a market for it."
It's not clear how the hackers got hold of this material - did they manage to breach Disney's hopefully robust IT security framework or was it a result of human error?
Either way, the ransom tactic is popular among cyber criminals - just as we have seen with the recent ransomware attack which caused havoc around the world.
The sad fact is that it's easy money for them. People often choose to pay simply because they just want their data back, whether it's a blockbuster movie or those irreplaceable family photos. These days our digital possessions are the new family silver.
However there is no guarantee, even if you do give in to the demand, that the criminals will keep their side of the bargain (they are criminals after all), or that you won't end up on a list of easy targets and be hit again.