Johnson has denied the allegations, calling them "absolutely not true." He did not return an e-mail or phone call on Monday seeking further comment.
Hundreds of thousands of Johnson's customers sought refunds from credit card companies, claiming they were charged for unauthorized purchases, according to the lawsuit.
When Visa and MasterCard fined I Works and related companies and terminated their accounts, the complaint says Johnson and others named in the lawsuit then created dozens of "shell" companies to accept card payments in order to avoid detection.
FTC attorneys say they also are preparing to ask a federal judge for a preliminary injunction against Johnson and the companies to prohibit them from further actions that might hurt consumers while the lawsuit proceeds. The agency also indicated it also might seek to freeze the operations' assets.
Federal court records also show that Johnson and I Works have been sued at least three times since 2003 over alleged violations of other firms' trademarks related to Internet-based businesses.
In 2003, eBay sued over misuse of its name, saying Johnson and his companies were offering services on how to make money on the online auction site with products called EBAY Solutions and EBAY Exposed.
The online auction and shopping website "has received numerous complaints from consumers regarding defendants' telemarketing calls," the company said in court documents, including pitches in which eBay's registered users were encouraged to patronize the website ebaysolutions.biz. Johnson settled by discontinuing use of the eBay name and agreeing to pay that company $10,000.
He has settled one other suit in a similar manner, and a third is pending.
Johnson also is known for his humanitarian efforts. After a massive earthquake struck Haiti in January, he flew doctors, food and supplies into the impoverished Caribbean nation and then flew orphans to Florida, where they met their adopting families. Later, when state parks ranger Brody Young was shot near Moab in November, Johnson flew his helicopter to help search for a suspect, and he also ferried supplies to residents stranded by floods in the St. George area last month.