Mr Murphy was speaking on the eve of tonight's contentious Question Time debate being screened by the BBC, which will feature BNP leader Nick Griffin.
The Cabinet minister said he regretted that the broadcast was going ahead, and he warned that, far from the BNP being an English problem, support for the far-right party had grown so much in Scotland that only the largest football stadiums could accommodate all its voters at once.
Last night, the BBC's watchdog, the BBC Trust, agreed to go ahead with the controversial programme. The broadcaster has even made contingency plans to relocate the filming of Question Time to a secret spot if there are threats to the safety of the guests and panellists.
Mr Murphy said the BNP won its seats in the European Parliament and had built its support base because of complacency. "I worry that Scotland is still too complacent. We look at parts of England where the BNP has won and I fear that people think it could never happen here.
"Ten years ago, the number of people voting BNP in Scotland numbered just over 3,000. In June of this year, that increased tenfold to 29,000 people in Scotland who decided to put their cross in the BNP box. If this thought doesn't concern people, then the problem is only going to get worse."
Mr Murphy said it turned his stomach that the BNP would be on television, but he urged politicians to take the threat from the party more seriously. "They must not convince themselves the BNP are not a danger in Scotland. The threat is there and we need to act," he said.
"All parties need to persuade good people that doing nothing helps those with extremist views. The overwhelming majority of politicians from all the main political parties are decent folk who, regardless of what I may think of their politics, have good intentions. The challenge for all these decent people is to prevent any anger with mainstream parties being exploited by people with evil intentions."
Michael Russell, Scotland's minister for culture, external affairs and the constitution, yesterday criticised the BBC. He said:
"Question Time is broadcast throughout the UK, and BBC managers in London must explain why they are bending over backwards to accommodate this overtly racist party, which has absolutely no standing north of the Border."
Last night, the SNP also called on BBC Scotland to follow BBC Wales and ban any broadcasts that include the BNP.
Spokesman Pete Wishart, MP, said: "The BNP thrive on the oxygen of publicity and they should not be allowed to peddle their odious and offensive views on prime-time television.
"The argument about allowing Nick Griffin on Question Time does not stand here, and BBC Scotland should follow their Welsh colleagues and rule out allowing any BNP representatives a platform on any Scottish programmes." The SNP and the other main parties in Scotland have refused to appear on any public platform with the BNP.
Meanwhile, the House of Commons has banned all MEPs from accessing Westminster because it could not block the BNP's two Euro members from having the same rights.
The decision, made in a late-night vote on Tuesday, was condemned by Scottish Conservative MEP Struan Stevenson, who said 70 MEPs would have their passes rescinded and would be seriously disadvantaged in representing their voters because of two BNP MEPs. He said: "The 25 Conservative MEPs represent every part of the UK and to do that effectively we need to have access to Westminster.
"All of us are, over on a fairly frequent basis, talking to members of the government. How on earth are we supposed to work closely with other parliamentarians when we've had our passes withdrawn? This is absolutely scandalous. It's not just a hammer to crack a nut – the whole situation is absurd and they really need to think again."
BNP supporters are expected to be in the studio audience in the BBC's Television Centre in west London for tonight's programme. Scores of anti-facist and pro-BNP supporters have also threatened to turn up outside.
BNP spokesman Simon Darby said the party would not rely on help from the Metropolitan Police to get Mr Griffin into the building. "We've got security in hand – we will sort our own security out," he said. Mr Darby insisted there would be no counter-demonstration by the BNP outside Television Centre.
Mr Griffin and his supporters want to avoid a repeat of ugly scenes that erupted outside parliament in June, when protesters pelted them with eggs and chased them down the street.
Question Time will be broadcast as usual from 10:35pm to 11:35pm on BBC1 tonight. Other panellists on the show include Justice Secretary Jack Straw and Liberal Democrat home affairs spokesman Chris Huhne.
There will also be two panellists from ethnic minority backgrounds: Muslim shadow community cohesion minister Baroness Warsi and the African-American writer and broadcaster Bonnie Greer.
ROCK STAR ATTACKS 'NAIVE' BBC
POP stars, writers and union members have condemned the BBC for allowing the British National Party a platform on Question Time.
Jerry Dammers, founder of The Specials, attacked the BBC as naive for giving BNP leader Nick Griffin a chance to express his views.
His words were echoed by former children's laureate Michael Rosen, who said people had a right not to hear the BNP's message.
Speaking during a rally held by Unite Against Fascism in London, Dammers said: "The BNP are hiding their true identity as Nazis … the BBC are allowing themselves to be used for that purpose."