The European Commission president was replying to a letter signed by MEPs, including Terry Reintke, who had called on the EU to examine ways for Scotland to rejoin the scheme despite Brexit.
However, in response Ms Von der Leyen has said it is “not possible” for Scotland to rejoin due to being part of the United Kingdom.
In her letter, she said: “The commission is aware of the Scottish Government’s statement on the UK decision not to associate to Erasmus+ and my colleague Mariya Gabriel has met Mr Richard Lochhead MSP, the Scottish minister for further education, higher education and science, who was keen to explore options for Scottish participation.
"However, as one constituent nation of the UK, association to Erasmus+ is not possible for Scotland, separately.
"The only possibility for the UK is to associate as a whole, or not at all."
Responding to the letter to Ms Reintke, Mr Lochhead said: “Thank you Terry and we look forward to continuing working with you and your European Parliament colleagues to explore how Scotland can retain as close a relationship as possible with Erasmus and our European friends.”
In January, Mr Lochhead held what was described as “productive talks” with Ms Gabriel, with the Scottish and Welsh governments criticising the replacement for Erasmus being brought forward by the UK Government.
The Turing Scheme will be launched in the UK and will cover much of the opportunities offered by Erasmus, but both governments said it was a “lesser imitation of the real thing”.
Responding in December to the news that Erasmus participation would be ditched as part of the UK’s Brexit deal with the EU, Mr Lochhead described the decision as a “huge blow”.
Reacting to the letter on Tuesday, the minister repeated that and said the problem was created by the UK Government.
He said: “Losing Erasmus is huge blow for the thousands of Scottish students, community groups and adult learners – from all demographic backgrounds – who can no longer live, study or work in Europe.
“The UK Government’s decision not to associate to Erasmus+ has created this problem and we are grateful to Terry Reintke and other MEPs for their continued support.
"Despite Scotland not being a state and therefore not being able to remain a full participant on the same terms as the UK at the current time, we will work with the EU institutions to explore the options for as close a relationship as possible being maintained.”
Alex Orr, policy adviser for the European Movement in Scotland, said: “We would urge the European Commission to reconsider its position, but noting admission to Erasmus for Scotland alone may not be possible, call on the UK Government to associate to the scheme as a third country, a position we are aware it previously rejected.
“A unilateral replacement, such as the proposed Turing scheme, will never be able to replicate the wealth of opportunities for all young people, or raise the same reciprocal benefits of the Erasmus Programme.”