This paper examines the impact of Brexit on international student migration. In a structural gravity model, we estimate student migration between 69 countries for counterfactual scenarios in which the United Kingdom leaves the European Union one year before the referendum. This exercise reveals a decrease in exchange students studying in the UK of around 3.8% to 4.9%. While the number of non-EU students to the UK rises, a drop in EU student numbers drives this result. Similarly, 30% to 38% fewer UK students choose to study abroad. The estimated changes in international student stocks show that most other member countries lose international students and non-EU countries host more than without Brexit. Our findings provide evidence that there may be hidden costs to Brexit affecting global student exchanges that we have yet to see.