Mr Marr clashed with the Home Secretary as he put forward concerns about the UK's hardline approach to leaving the EU.
He listed a number of industry bodies worried about what will happen when the country leaves the bloc, including representatives from the chemical, aerospace and food sectors.
He said: “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.
“They said that this proposal is a serious risk to manufacturing competitiveness and will result in huge new costs and disruption to UK firms.”
Responding to the facial expression of Ms Patel, who was being interviewed via video link, he then added: “I can’t see why you’re laughing.”
However, the Home Secretary was not seen to be laughing during the exchange.
He went on: "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 really big challenge to this plan.”
Ms Patel was criticised on social media for appearing to "smirk" during the serious discussion, however others defended her.
One person wrote: "Priti Patel smirking as Andrew Marr reads out warnings from manufacturers about the potential dire economic impact of a no-deal Brexit on their business."
“I can’t see why you’re laughing” says Andrew Marr to Home Secretary Priti Patel as she smirks whilst he reads out the manufacturing industries dire warnings on her Government’s Brexit proposals pic.twitter.com/hFKi4nJKZE— Peter Stefanovic (@PeterStefanovi2)October 13, 2019
Priti Patel smirking as Andrew Marr reads out warnings from manufacturers about the potential dire economic impact of a no-deal Brexit on their business.
Marr: “I’m not sure why you’re laughing.”— Adam Bienkov (@AdamBienkov)October 13, 2019
However Tory MP Nadim Zahawi said: "She is neither smiling or laughing. I guess some people are so incensed at the thought of a [government] that is upholding the Democratic will of the people, they are willing to use any means necessary to demonise its ministers."
I watched this earlier and watched it back and I don’t get it... she’s not laughing? https://t.co/MqOanVnMEJ— Jane Merrick (@janemerrick23)October 13, 2019
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."
During the interview she also said security measures were being stepped up in preparedness for a possible no-deal Brexit but denied they were driven by fears of an upsurge in terrorism by dissident Irish republicans.
She acknowledged however they were "conscious" of the situation in Northern Ireland and said ministers were working on "alternative arrangements" for intelligence and data sharing.
"When it comes to security tools and security co-operation there are many measures that are being put in place right now in preparedness for no-deal," she told BBC1's The Andrew Marr Show.
"Specifically to Northern Ireland, we are conscious and we are working with all organisations, agencies, to ensure that we remain safe."
Labour leader Jeremy Corbyn said the party would decide how to respond once they had seen any deal Mr Johnson was able to bring back from Brussels.
However, he urged "caution" on any MPs considering backing an agreement if it were put to a confirmatory referendum.
"I think many in Parliament, not necessarily Labour MPs but others might be more inclined to support it even if they don't really agree with the deal. But I would caution them," he told Sophy Ridge on Sunday.