Britons have been told that they must start the paperwork for taking pets abroad on 1 September 2020 at the latest if they plan to travel on 1 January 2021.
During the Brexit transition period, Britons can continue to use the existing Pet Passport system to travel with their pets.
However, new processes could be introduced after the transition period ends on 31 December 2020, which could render the current documents invalid.
The changes will affect domestic pets as well as service animals.
A statement from the Department for Environment, Food & Rural Affairs said: "The UK government is working with the European Commission to ensure a similar arrangement for pet travel between Great Britain and the EU from 1 January 2021.
"However, if an agreement is not reached there could be new requirements in place for those travelling with a pet from Great Britain to the EU from 1 January 2021.
"If pet owners are planning to travel from January 2021 onwards then they should contact their vet at least four months in advance of their travel date to discuss the latest requirements, including the documentation and vaccinations needed.
"For example, those wishing to travel with their pet from Great Britain to the EU on 1 January 2021 should discuss the relevant documentation their vet by 1 September at the latest."
To further confuse the situation, it's not entirely clear what paperwork is needed at the moment.
Great Britain – which includes England, Scotland and Wales – will become a "third country" from 1 January 2021. Under EU law, a third country is "a country that is not a member of the European Union as well as a country or territory whose citizens do not enjoy the European Union right to free movement."
There are three different categories of third country under the current EU Pet Travel Scheme: unlisted, Part 1 listed, Part 2 listed. The rules and regulations applicable to each category is different.
The UK government has applied to be a listed country, but at present it's not clear which category Great Britain will fall into.
Pet owners are advised to check the latest pet travel advice before they travel.
Once the Brexit transition period ends, a number of changes will come into effect, which could increase the cost and amount of red tape travellers have to face to enter EU countries.
The European Health Insurance Card (Ehic) scheme, for example, looks like it will not continue for Britons, which would mean higher travel insurance costs for many travellers.