Cheney predicted "In My Time: A Personal and Political Memoir" would be a sensation that would cause heads to "explode" -- language Powell took exception to in an interview on CBS's "Face the Nation" program.
"My head isn't exploding, I haven't noticed any other heads exploding in Washington DC," said Powell, who scathingly suggested this was the kind of language expected from a supermarket tabloid, not a former vice president.
The two Bush-era heavyweights have often traded blows and the roots of their disagreement go right back to the Iraq war and the policy that led to the 2003 invasion that ousted Saddam Hussein.
Powell said Cheney alleged that as secretary of state he had withheld his best advice from Bush while offering stinging critiques of the president's policies to others.
"That's nonsense. The president knows that I told him what I thought about every issue of the day," he said.
Powell also accused Cheney of seeking to smear his successor as secretary of state, Condoleezza Rice, as well as ex-CIA director George Tenet.
"He's taken the same shots at Condi, with an almost condescending tone. She tearfully did this, or that. And he's taken the same shots at George Tenet," said Powell, who, like Cheney, was a Republican appointed by Bush.
Cheney, in his memoir, condemns Powell's stance on the Iraq War, but the former military man -- who also served as chairman of the joint chiefs of staff and national security adviser -- brushed aside the critique.
"Mr. Cheney may forget that I'm the one who said to President Bush, 'if you break it you own it'," he said, adding pointedly: "Mr. Cheney and many of his colleagues did not prepare for what happened after the fall of Baghdad."
Cheney, vice president at the time of the September 11, 2001 attacks, was seen as one of the biggest hawks in Bush's administration as the United States launched its invasion of Afghanistan and later of Iraq.
Powell added: "Mr. Cheney is free to say what he wishes, but so far I haven't seen anything in it that is as explosive as he claims it is, and I don't see any heads laying on the street."