Russian hacking group REvil published on their dark web headquarters, Happy Blog, that they had accessed Copeland's firm and presented a string of screenshots as alleged evidence.
The gang has previously threatened to auction off data allegedly stolen from pop star Madonna, released legal documents relating to Lady Gaga, and tried to extort Donald Trump.
The group uses ransomware - a type of software often unknowingly installed by the victim - to break into a networks and encrypt them.
Copeland, 83, who has an estimated net worth of $760million, based in Texas, heads up Kenneth Copeland Ministries (KCM) and is one of the world's wealthiest pastors.
He has risen to notoriety in 2020 after a string of bizarre claims about the coronavirus pandemic.
Hackers claim they managed to get inside KCM's systems and steal more than 1.2tb of data, the equivalent of around 120,000 storage boxes of files.
Screenshots show banks of alleged computer files with labels such as "budgets", "projects", "payroll" and "inventory".
Writing in broken English, hackers threaten the data "will soon be made public".
They claim to have "financial documents, contracts, bank documents, sales history, emails, bases, geo documents".
"Money, authority religion and again money. A success story. Absolutely all severs and working computers of the company are hacked and encrypted," the cyber criminals claim.
It is understood the listing has now been taken down from the site on the dark web.