Cain, 74, was diagnosed with the disease in late June and later hospitalized after attending a Tulsa, Oklahoma, rally for President Donald Trump, where many attendees crowded close together without wearing face masks to prevent the spread of the novel coronavirus.
He spent most of July in an Atlanta-area hospital.
"We're heartbroken, and the world is poorer: Herman Cain has gone to be with the Lord," the statement on his website said.
Cain, who called himself an ABC man - "American Black Conservative" - had just started hosting a new show on Newsmax TV and hoped to play a role in the 2020 presidential election campaign, the statement said.
Cain started his career as a civilian employee for the US Navy and worked for Pillsbury and Burger King before becoming chief executive of Godfather's Pizza.
He made national headlines in 1994 when he sparred with then-President Bill Clinton about healthcare costs facing small business owners during a televised town hall meeting.
"Herman Cain embodied the American Dream and represented the very best of the American spirit," White House spokeswoman Kayleigh McEnany said in a post on Twitter. "We will never forget his legacy of grace, patriotism, and faith."Ronna McDaniel, chairwoman of the Republican Party, noted Cain's passing in a tweet, saying, "Please keep the entire Cain family in your prayers."