A "transition period" after the UK leaves the EU should not continue beyond 31 December 2020, Brussels says.
The UK has said the temporary arrangement should last for about two years after Brexit in March 2019.
Terms of the transition period, which the UK calls an implementation phase, have yet to be negotiated between the two sides.
The EU says the UK will have to continue to follow its rules and cannot adopt an "a la carte" approach.
It has just published its guidelines for the next phase of Brexit negotiations.
These talks will initially focus on agreeing the precise terms of the transition phase, before moving on to the UK and EU's long-term future relationship.
What is a transition phase?
It will be a temporary period after the UK leaves the EU and before the final arrangements kick in. Both sides have talked about having such an arrangement, although they use different names for it.
The UK says the "implementation phase" will avoid a "cliff edge" for businesses on Brexit day.
The European Commission's guidelines state that the UK should continue to follow EU law and stay in the European customs union and single market during the transition phase. Rulings of the European Court of Justice will continue to apply, it says.
"The transition period needs to be clearly defined and precisely limited in time," the EU says.
"The commission recommends that it should not last beyond 31 December 2020."
This date marks the end of the EU's seven-year budget cycle.
Long-term, the UK has already said it plans to leave the customs union and single market and end the supremacy of EU court rulings as part of Brexit.
Some Brexit-supporting Tory MPs have warned the UK could become a "colony" of the EU during the transition period if it continues to closely follow the same rules.
Responding to Mr Barnier's comments, Business Minister Claire Perry said the EU had already made "various grand statements" and that much of what he had said was a "negotiating stance".
She said the most important thing was "complete agreement" of the need for a transitional deal.