The EU negotiator made the astonishing warning pets would be barred from crossing the Channel in the event of Brexit negotiations failing.
He claimed crashing out of the bloc would have “consequences in multiple areas” from “the capacity of British planes to land in Europe to that of dogs and cats to cross the Channel”.
Tory Eurosceptic Jacob Rees-Mogg slammed the comments as “really very silly”.
He told the Telegraph: “You can’t take this man seriously, he is now negotiating absurdly.
“It undermines his credibility.”
Under current rules, Britons need a pet passport for their animals which confirms they have been vaccinated against rabies.
Mr Rees-Mogg added: “The worry has always been of rabid animals coming from the Continent.
“I’m all for keeping rabid eurocrats out of the UK.”
Concerns about planes landing in Europe have also previously been dismissed by airline chiefs, who insist there will be no problems.
Mr Barnier told told French paper Le Journal du Dimanche that no deal was not his “preferred option” but plans were being made just in case.
He said: “It’s a possibility. Everyone needs to plan for it, member states and businesses alike.
“We too are preparing for it technically.”
It comes after Mr Barnier gave the UK a two-week deadline to clarify its divorce bill position so negotiations can finally move on to trade.
Last week, Mr Barnier insisted he wanted a clearer undertaking than May gave in September on how far Britain would “honour” its financial obligations.
He said: ”It is absolutely vital if we are to achieve sufficient progress in December.
“If that’s not the case, then we will continue and that will pull back the opening of discussions on the future.”
Brexit Secretary David Davis said yesterday that Britain would not offer a figure or formula for how much the UK owes.