Britain is "too lazy and too fat" with businessmen preferring "golf on a Friday afternoon" to trying to boost the country's prosperity, Liam Fox has said.
The international trade secretary's remarks, at a Conservative Way Forward event, were recorded by the Times.
Downing Street said he was clearly expressing private views.
Richard Reed, Innocent Drinks co-founder, said Mr Fox "had never done a day's business in his life".
Mr Fox, who was a prominent voice within the Leave campaign in the EU referendum, is in charge of negotiating trade deals for the UK once it has left the European Union.
During his speech to activists on Thursday evening he said there needed to be a change in British business culture and said people had got to stop thinking about exporting as an opportunity and start thinking about it as a duty.
"This country is not the free-trading nation it once was. We have become too lazy, and too fat on our successes in previous generations," he said.
He added: "Companies who could be contributing to our national prosperity - but choose not to because it might be too difficult or too time-consuming or because they can't play golf on a Friday afternoon - we've got to be saying to them if you want to share in the prosperity of our country you have a duty to contribute to the prosperity of our country."
In Mr Fox's speech he also criticised the "Foreign Office view of the world" for focusing on capital cities and diplomacy rather than business, and claimed his new government department had taken charge of "trading elements".
The comments follow his letter to Foreign Secretary Boris Johnson, which was leaked to the press, suggesting British trade would not flourish unless the Foreign Office was reduced to a department focused only on diplomacy and security.
Liam Fox says that UK exporters are too often on the golf course to focus on selling their wares overseas.
Analysis - By Joe Lynam, business correspondent
No-one knows how much business is done on the front or back nine - or more plausibly in the clubhouse over a glass of something - but it's probably not insignificant.
Business bibles such as Forbes, CNBC and Bloomberg all have special features about golf and its importance to sealing a deal.
People do business with other people and golf is a game which relies on honesty, temperament and sound judgement. Cheating is shunned. Deciding whether to do a deal with someone can require similar attributes.
Setting aside your clubs for a moment though, many business people will have been galled to be told that they are too lazy not to be exporting and that it is their duty to be doing so.
The notion that entrepreneurs couldn't be bothered to increase their sales will irritate - especially when it comes from a politician who has never run a company.
A Downing Street spokesman said Mr Fox had been expressing his own views at the event, and not the views of the government.
A source at No 10 later added: "Whatever form of words we use, the point we all want to make is that Britain can trade its way to greater prosperity, with the well-paid jobs and security that entails."
Mr Fox's own spokesman said the minister was committed to supporting the full range of businesses in the UK so they could best take advantage of the opportunities that Brexit presented.
But Mr Reed, who was also deputy chair of the official Remain referendum campaign, called Mr Fox's comments "absolutely disgusting".
"He is a representative of us, of this country, and he turns round and slags us off, calling us fat and lazy," he said on BBC Radio 4's Today. "He's never done a day's business in his life."
"He's talking about business people here who were absolutely clear in saying that we want, and do, export, and that's why we do want to remain in the EU... I just think: 'how dare he talk down the country that he damaged, how dare he'.
"He's a terrible, terrible voice for British business."
Mr Reed added that he'd "never played golf in [his] life".
Labour MP Chuka Umunna said Mr Fox's comments were "a complete disgrace, coming from the man supposed to be promoting our businesses globally" and UK businesses deserved an apology.
"UK business must have woken up today, read Liam Fox's comments, and thought with friends like these who needs enemies", he tweeted.
The chief executive of the Engineering Employers Federation, Terry Scuoler, said: "The comments from Liam Fox were extremely unwise and very unhelpful.
"What we're looking for in these uncertain times is support from government - not negativity - particularly through the forthcoming Autumn Statement."
'Offensive and crass'
Shadow minister without portfolio Jonathan Ashworth said Mr Fox lacked "humility" and should apologise.
"These are offensive and crass comments," he said.
"Every MP knows of hard working businesses in their constituency who are struggling at the moment. None of them are lazy or more interested in playing golf."
Pat McFadden, Labour MP and supporter of the Open Britain campaign group pushing for a close relationship with the EU, said he was sceptical about how Mr Fox could fulfil his role.
"If the government doesn't confirm it supports membership of the single market it won't serve British business, but that is hardly surprising if ministers can't even speak up for British business," he said.
"It is hard to see why the government's trade minister is attacking British business when he is supposed to be promoting the UK as a great place to do business."
However, Mr Fox received support on Saturday from a variety of business leaders, with John Longworth, ex-director general of the British Chambers of Commerce, saying that companies had to contribute to making a success of Brexit.
He told the Daily Telegraph: "The government of post-Brexit Britain has a unique opportunity to make the UK the best place in the world to do business - and business itself has to step up to the plate and make this happen."
Peter Hargreaves, founder of financial services company Hargreaves Lansdown, also backed Mr Fox, saying: "We have a lot of very good entrepreneurs in Britain, but there's no doubt that there are also some in boardrooms who don't deserve to be there - they're idle, incompetent and ineffective."
He described Mr Fox's comments as "just the right kick in the pants", adding that "the so-called experts and the doomsayers should shut up and stop trying to talk us into a recession".