The pro-European cabinet minister said UKIP had no positive policies and was just "against" foreigners.
UKIP leader Nigel Farage hit back by accusing Mr Clarke of holding millions of British people "in utter contempt".
He said Mr Clarke was "obviously not interested" in winning back disaffected Tory voters at Thursday's local elections in England and Wales.
It comes as UKIP accused the Tories of conducting a "morally reprehensible" smear campaign against its local election candidates.
The anti-EU party has expanded rapidly, recruiting a record 1,732 candidates to contest Thursday's local elections.  It admits it has not had the time or money to vet all of them properly.
UKIP says it has evidence that smears about its candidates are being spread by Conservative Central Office, which it claims has been trawling would-be UKIP councillors' Twitter and Facebook pages for months.
"Were we inclined to return the favour, we would find even more examples to use against them.
"We deem that using our candidates as cannon fodder to undermine a political campaign (is) morally reprehensible and downright dirty," said a spokesman.
The party is investigating six candidates over links to the BNP and other far right groups or alleged racist and homophobic comments, following stories in national and local newspapers.
"I am glad they have found some candidates in the BNP because we don't want them. We are quite pleased. We don't want these people in the party," a UKIP spokesman said.
He said the row showed the Conservative Party was "rattled" by UKIP, which is hoping to make significant gains in Tory heartlands on Thursday, but added: "This isn't scrutiny, it's smear."
Asked on the BBC's Andrew Marr show about UKIP's claims, Transport Secretary Patrick McLaughlin said all candidates had to be scrutinised, but added: "I don't know anything about a smear campaign."
But his cabinet colleague, Ken Clarke, minister without portfolio, added fuel to the row in an interview with Sky News.
He said: "They of course have not been able to vet their candidates. Fringe right parties do tend to collect a number of waifs and strays...
"Some of them are saying quite different things now they are in politics than their actual views."
Asked whether he agreed with David Cameron's 2006 claim that UKIP was made up of "fruitcakes and closet racists", Mr Clarke replied: "I have met people who satisfy both those descriptions in UKIP.
"Indeed, some of the people who have assured me they are going to vote UKIP I would put in that category. I rather suspect they have never voted for me."
Mr Clarke said he was sure that "most of the UKIP people are perfectly nice when they are having a drink".
But he added: "The trouble with UKIP really is it is just a protest party.
"It is against the political class, it is against foreigners, it is against immigrants. But it does not have any very positive policies. They do not know what they are for."
He added: "The temptation to ordinary voters to UKIP is these are very difficult times, the political classes are regarded as having got us into a mess.
"It is very tempting to vote for a collection of clowns or indignant, angry people, who promise that somehow they will allow us to take your revenge on people who caused it."
Conservative backbencher Nadine Dorries criticised Mr Clarke's intervention, saying in a Twitter message: "I suppose Ken Clarke's strategy of being rude to and insulting Tories about to vote UKIP means we don't want them back for general election?"
UKIP leader Nigel Farage echoed Ms Dorries' comments, saying: "It is obvious that Mr Clarke holds millions of people in this country in utter contempt.
"UKIP are attracting supporters from all three main parties and, significantly those who have either not voted for over 10 years or have never voted before in their lives.
"Instead of slagging them off maybe he should try to wrap his head around the idea that UKIP are appealing to people due to the failure of the bloated self-satisfied political machine of which he is such a typical member.
"He obviously doesn't care and isn't at all interested in attracting those millions to vote for the Conservatives, well so be it. The way things are going they won't be doing so any time soon."
Lib Dem leader Nick Clegg said UKIP was a "very seductive" option for people who wanted to say "to hell with mainstream politics" but he urged voters to look at the party's policies.
UKIP has also dismissed claims in The Observer that the party's policy-making process in chaos.
The newspaper published leaked e-mails between party treasurer Stuart Wheeler and MEP Godfrey Bloom, in which Mr Bloom advises UKIP to adopt policies "off the shelf" from right-wing think tanks, because trying to reach agreement on where it stood on issues was like "herding cats".
A UKIP spokesman said: "I am glad they are discussing policies. So they should be."
Veteran Tory Ken Clarke has waded into his party's war of words with UKIP by branding them "a collection of clowns".