Halfway through reading out a list of industry groups who have raised concerns in a letter to the Government about the impact of a no-deal Brexit, Mr Marr stopped and said to Ms Patel: "I can't see why you are laughing."
Ms Patel, who was being interviewed over video link rather than in the studio, could be seen smiling as Mr Marr spoke of the industry representatives' concerns.
The Home Secretary did not respond to the comment.
Mr Marr's comment came as Ms Patel had been defending the Government's negotiating position with the EU.
He said industry bodies at the "forefront" of the economy, including representatives from the chemical, aerospace and food sectors, had raised concerns that a no-deal Brexit posed a "serious risk to manufacturing competitiveness".
Mr Marr said: "The Government's own modelling suggests that this Free Trade Agreement would result in a lower growth of 6.7%. Is that something that you're prepared to accept as a price worth paying?"
Ms Patel responded: "Well, I don't accept that, and you know, I don't know which data you're quoting."
After Mr Marr informed Ms Patel that it was from the Government's own documents, she continued: "Well, Andrew, there's been a range of information that has been put out in the media over recent weeks and months, much of which, I should say, is out of date.
"And as someone that sits, someone who sits on the Cabinet committee every single day, where we're looking at the preparations for Britain post-Brexit, preparing for a no deal as well, you know, we have every confidence in our economy, in our businesses, but also in terms of future prospects post-Brexit."
Mr Marr then proceeded to read out a list of industry representatives who had raised concerns about the prospect of a no-deal Brexit.
He said: "OK, let's hear from those businesses directly then, because a whole bunch of them, and I'll read them out, the Society of Motor Manufacturers and Traders, the people that make and sell cars; the Chemical Industries Association; the Food and Drink Federation; the Association of the British Pharmaceutical Industry, and the Aerospace Trade Industry body, a lot of people who are actually at the forefront of trying to make this country earn its place in the world, sent a letter to the Government, which I will now read out part of to you.
"And they've said that this proposal 'is a serious risk to manufacturing competitiveness and will result in huge new costs and disruption to UK firms'.
Pausing in the middle of reading the extract from the letter, Mr Marr turned to a television screen showing Ms Patel on a video link and said: "I can't see why you're laughing."
He then continued: "'It's got the potential to risk consumer and food safety and confidence, access to overseas markets for UK exporters and vital future investment in innovation in this country'. That is a really serious challenge to this plan, is it not?"
Ms Patel did not acknowledge the comment from Mr Marr, merely replying that the Government has been making preparations to mitigate any potential impact of a no-deal Brexit.
She said: "Well, this is why the Government has been working assiduously, with business as well I should say, across a range of sectors when it comes to planning for our exit from the European Union."
Conservative MP Nigel Evans (Ribble Valley) has spoken out, criticising Mr Marr's interview with Ms Patel.
He told the PA news agency: "Priti Patel and the Government are fed up with 'project fear' stories and being hammered by journalists who are critical because a Government is working tirelessly to deliver what people voted for in the 2016 referendum.
"Andrew Marr should be inviting Labour politicians onto his show on a weekly basis and pillorying them for reneging on their 2017 election promises to deliver Brexit and doing everything in their power to stop it.
"There is no Brexit crisis in Britain, only a democratic crisis, and they fear a deal being agreed between Boris Johnson and the EU which will expose them for what they are."
Responding to the interview on social media, Labour MP David Lammy (Tottenham) said it was "unforgiveable" that Ms Patel did not know the Government's analysis regarding the potential impact of a no-deal Brexit.
Mr Lammy said: "Priti Patel is reminded of her own government's analysis of the disastrous impact of Boris Johnson's proposed Brexit, she replies "I don't know which data you're quoting".
"With people's jobs and livelihoods on the line, this is unforgivable."