The health secretary said interventions from the likes of Airbus only increased the chance Britain would end up with a “fudge”.
His comments are the strongest criticism yet from a government frontbencher.
On Friday, the aerospace giant announced it was making plans to leave the UK in the event of a “no deal” Brexit.
Siemens also criticised the government for presiding over “two years of not having achieved what we were promised, which is that this was all going to be easy”.
Mr Hunt told the BBC’s Andrew Marr Show: “I just thought it was completely inappropriate for businesses to be making these kind of threats for one simple reason.
“We are in an absolutely critical moment in the Brexit discussions and what that means is we need to get behind Theresa May to deliver the best possible Brexit – a clean Brexit.
“What businesses want, and I was in business for 14 years, what they want is clarity and certainty.
“The more we undermine Theresa May, the more likely we are to end up with a fudge, which I think would be a disaster for everybody.”
He added it was not “particularly surprising” that “multinational companies have qualms about Brexit”.
Blasting the EU for its warnings about the progress of negotiations, Mr Fox urged people to “stand firm in this situation, ignore these siren voices”.
Liam Fox, the international trade secretary, gave a gentler warning to businesses speaking out about the effects of Brexit and their plans to relocate staff.
He told Sky News’ Sophy Ridge on Sunday: “Companies are right to say if there’s no deal that won’t be good for Britain.
“But it won’t be good for Europe either, and the point I make to them is that they should also be making the same case to European governments – that that will be bad for them in an era when we have complex integrated supply chains it will be necessarily bad for both sides.”
Last year he claimed that striking a free trade deal with the bloc would be the “easiest in human history”.
He doubled down on the remark on Sunday, telling Sky News: “The trade part of it should be technically easy – because we already have full regulatory and economic alignment with the EU.
“But of course this was never just going to be about trade, it’s mostly about politics; it’s about the politics of the EU, and that’s the complicated factor in all of this.”
Dr Fox also said he would be prepared to accept a longer Brexit transition under certain conditions.