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In the first two decades of the 21st century, a wide range of analyses, including free volatile carboxylic acids (FVCAs), endeavoured to describe 10 different cheese varieties from Switzerland. The aim of the present work was to investigate whether these 10 cheese varieties could be classified by means of supervised machine learning (ML) techniques, as well as to analyse the importance of the features FVCAs in order to understand their role in characterising cheese varieties. Special emphasis was placed on SHAP values (SHapley Additive exPlanations). In total, 241 cheese samples were classified using different ML algorithms with the help of the PyCaret library; at least 90% were correctly classified with two ensemble algorithms: Extra Trees and Random Forest. The fewest misclassifications were observed for Emmentaler AOP, Raclette du Valais AOP, and Formaggio d’Alpe Ticinese DOP, whereas most misclassifications occurred between Le Gruyère AOP and Berner Alpkäse AOP. The most important feature was C1, followed by C3, C6, and iso-C4, with iso-C6 being the least important after C2 and C4. By means of the interpretation of SHAP values applied as a differentiating feature, key FVCAs were identified for most cheese varieties. This study represents a first step towards improved differentiation of cheese varieties.