The European Union has ruled out allowing Welsh students to stay in its international study programme.
The UK government chose not to continue with the EU's Erasmus scheme as part of the Brexit deal.
Welsh and Scottish ministers had hoped to find a way to allow students to continue "benefitting" from the scheme.
EU Commission president Ursula von der Leyen said the only way Wales could continue was if the "whole" of the UK rejoined.
Millions of students across Europe have taken part in Erasmus since its inception in 1987, with the exchange scheme allowing students to study at thousands of educational institutions across more than 30 countries.
In a letter to a Member of the European Parliament [MEP], Ms von der Leyen said: "The EU offered the United Kingdom full association to the Erasmus programme in exchange for the standard financial contribution from third countries participating in union programmes.
"Following a year of constructive negotiations with the UK government, the decision was made in London not to pursue UK association to Erasmus.
"As one constituent nation of the UK, association to Erasmus is not possible... separately.
"The only possibility for the UK is to associate as a whole, or not at all."
With Northern Irish students being allowed to continue to participate under an arrangement with the Irish government, more than 100 MEPs signed a letter in January asking the EU Commission to consider extending "the benefits of Erasmus programme to students and young professionals in Scotland and Wales".
Following the EU Commission's response, Terry Reintke, the German Green MEP who organised the letter, said the response was not what MEPs "had hoped for" but they would "continue to explore how Scotland and Wales could stay in Erasmus".
Earlier this month, the UK government announced an initial £110m investment in its worldwide replacement Turing scheme.
Welsh Secretary Simon Hart said: "The Turing scheme will give students in Wales the support and opportunity to study and work abroad, no matter their background, by boosting access to student exchanges across the globe."
Speaking in the Senedd earlier this month, First Minister Mark Drakeford accused the UK government of a "small-minded approach" in withdrawing form the Erasmus scheme, which he described as "one of the jewels of the European Union".
He added he had discussed "bilateral possibilities for exchanges" with the German ambassador and the Irish foreign minister.
An Irish government spokesman said: "It is very early stages in engagement post-Brexit, and Ireland is determined enhance its relations with the devolved administrations in the UK."
A Welsh Government spokesman said: "We continue to explore all options to ensure highly-valued partnerships with Europe, that have been damaged by the UK Government's decision not to participate in Erasmus, are able to continue."