Apparently (according to the NYT) "Disney, which bought Miramax more than a decade ago, has a contractual agreement with the Miramax principals, Bob and Harvey Weinstein, allowing it to prevent the company from distributing films under certain circumstances, like an excessive budget or an NC-17 rating.". They also say
"Mr. Moore’s agent, Ari Emanuel, said Michael D. Eisner, Disney’s chief executive, asked him last spring to pull out of the deal with Miramax. Mr. Emanuel said Mr. Eisner expressed particular concern that it would endanger tax breaks Disney receives for its theme park, hotels and other ventures in Florida, where Mr. Bush’s brother, Jeb, is governor."
Michael Moore himself has written on his website about this in his own inimitable style. Ironically whilst Disney is trying to block the film in the US it appears that it will be distributed to other countries, they (fortunately) do not appear to be able to prevent that. Unfortunately this isn’t a case where the US’s famous "First Amendment" applies as this isn’t the US Government trying to supress expression, it is a corporation and so it doesn’t apply here.