This means the popular game won’t be available for new users to download on iPhones or other Apple devices.
Mr Sweeney called out Apple in a series of tweets and said the appeals process may take about five years to complete.
The BBC has approached Apple for comment.
People who already have the game downloaded on their Apple devices will be able to carry on playing it, but will not receive any updates.
Fortnite was originally removed from Apple’s App Store last year for violating its policies by launching its own in-app payment system.
Apple charges a 30% commission on all in-app purchases, but this feature tried to bypass that.
The move triggered a legal battle brought by Epic Games, which accused Apple of running the App Store as a monopoly.
