Environment Secretary George Eustice said owners will not be able to use their EU pet passports once the current Brexit transition period finishes at the end of the year.
Instead, he said he expected they would have to get a certificate from a vet confirming their pets’ rabies vaccinations were up to date before travelling.
However he indicated UK owners should avoid more onerous restrictions which would have meant obtaining a blood sample and sending it to an EU-approved laboratory at least three months in advance.
The Government had applied for the UK to be in Part 1 of the EU Pet Travel scheme, which would have meant little change to the current arrangements, however Mr Eustice said it was more likely to be in Part 2.
“We’re likely to be listed in the EU’s annex 2, the sort of second category, which means whereas in the past you might have had a pet passport, in future you’d need a certificate from the vet instead of the passport,” he told BBC One’s The Andrew Marr Show.
“It won’t be as easy as having the passport because you’d need to go to the vet prior to leaving rather than have the passport that shows your rabies vaccines are up to date.”
Under the Part 2 rules, owners need to visit an official vet no more than 10 days before travelling to get an animal health certificate confirming their pet has been microchipped and vaccinated against rabies.
Blanche Shackleton of the charity Guide Dogs said they were “extremely disappointed” and that travel to Europe would become “far more disruptive and difficult” for people with sight loss.
“Guide dog owners could now face restrictions on their travel to Europe, including only being able to leave and re-enter the UK through a limited number of routes, and having to navigate a complex certification process for their guide dog every time they travel,” she said.
“As well as travel to Europe, we urgently need clear information on whether there will be changes to the process of travel to Northern Ireland from other parts of the United Kingdom.”