Richard Lochhead reaffirmed in his letter that the Scottish Government will pay tuition fees for eligible students from the EU, EEA and Switzerland, starting courses this year or next, for the duration of their courses.
Scotland has proportionally more EU students than any other part of the UK, with some in the higher education sector fearing that Brexit could put off applicants from overseas.
The letter from the SNP MSP also makes the case for Scottish institutions continuing cross border research and collaboration through Horizon 2020 and other relevant European programmes after Brexit.
"Inward migration has made an overwhelmingly positive contribution to Scotland’s higher and further education institutions and research institutes as well as businesses. It is crucial that EU staff and students can continue to have freedom of movement and protection of the rights that they already have here.
"We do not agree that EU citizens should have to apply to the Settlement Scheme – the UK Government should immediately guarantee the rights of EU citizens in the UK."
Last week, the SNP claimed that the international reputation of Scots universities as being among “the best in the world” was in jeopardy over the prospect of EU students being forced to leave the country before their studies end.
Constitutional secretary Michael Russell accused the UK government of being “ignorant or incompetent” over the post-Brexit plan, which would see students allowed to stay for just three years of study – despite most Scottish degrees lasting four years.
The UK government has insisted its post-Brexit plans are geared towards improving wages and university applications have never been higher.