"A former Speaker of the House is threatening jail time for members of Congress who are investigating the violent January 6 attack on our Capitol and our Constitution," the Wyoming Republican on the Democrat-led committee said.
"This is what it looks like when the rule of law unravels."
Gingrich, who led the House through Bill Clinton's impeachment trial, spoke with Fox News's Maria Bartiromo on Sunday morning where he blamed Attorney General Merrick Garland and the Capitol riot panel of "running amok" and ``breaking the rules."
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He compared the board to a "lynch mob" before surprisingly claiming without evidence that the members of Congress on the panel could be jailed in the new Congressional term on January 4, 2023 -- after an election that multiple polls have suggested might be a red wave.
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"I think when you have a Republican Congress, this is all going to come crashing down, and the wolves are going to find out that they're now sheep. And they're the ones who are, in fact, going to, I think, face a real risk of jail for the kind of laws they're breaking," Gingrich said.
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It's not clear what crime the committee, which has been relatively transparent with its examination, has achieved.
But Gingrich said the panel is "running over people's" civil liberties' and suggested that a new GOP-dominated Congress would turn the tables against the investigators themselves.
"All these people who have been so tough and so mean and so nasty are gonna be delivered subpoenas for every document, every conversation, every tweet, every email," the former Georgia lawmaker threatened.
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"Because I think it's clear that these are people who are literally just running over the law, pursuing innocent people, causing them to spend thousands and thousands of dollars in legal fees for no justification, and it's basically a lynch mob."
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He added: "And, unfortunately, the attorney general of the United States has joined that lynch mob and is totally misusing the FBI."
Gingrich's time in Congress overlapped with Cheney's father's time, former Vice President Dick Cheney, who held her seat as Wyoming's lone representative from 1979 to 1989.
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Democrat Rep. Zoe Lofgren of California, Cheney's fellow January 6 committee member, said Gingrich's penal threat was "just bizarre" in an interview with CNN later on Sunday.
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"I think Newt has really lost it. You know, it leaves me speechless," Lofgren told CNN host Jim Acosta.
She added, "and he looks terrible."
Gingrich's opinion may reveal where the GOP is aiming as the midterm season approaches.