The Hollywood Reporter said the figure is four times greater than previous estimates.
The film was No. 1 at the U.S. box office when it was released last weekend, earning $85 million.
"Piracy is a serious issue for us. We now estimate that there are above 4 million downloads of that stolen 'Wolverine' movie that was up there," the entertainment industry trade newspaper quoted News Corp. Chief Operating Officer Peter Chernin as telling Wall Street analysts via conference call Wednesday.
Chernin said many of the Web sites that made "Wolverine" available without authorization have been shut down.
An investigation into who is responsible for the leak is under way.
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