Two-dimensional (2D) materials have been a central focus of recent research because they host a variety of properties, making them attractive both for fundamental science and for applications. It is thus crucial to be able to identify accurately and efficiently if bulk three-dimensional (3D) materials are formed by layers held together by weak binding energy and, thus, can be potentially exfoliated into 2D materials. In this work, we develop a machine-learning (ML) approach that, combined with a fast preliminary geometrical screening, is able to efficiently identify potentially exfoliable materials. Starting from a combination of descriptors for crystal structures, we work out a subset of them that are crucial for accurate predictions. Our final ML model, based on a random forest classifier, has a very high recall of 98%. Using a SHapely Additive exPlanations (SHAP) analysis, we also provide an intuitive explanation of the five most important variables of the model. Finally, we compare the performance of our best ML model with a deep neural network architecture using the same descriptors. To make our algorithms and models easily accessible, we publish an online tool on the Materials Cloud portal that only requires a bulk 3D crystal structure as input. Our tool thus provides a practical yet straightforward approach to assess whether any 3D compound can be exfoliated into 2D layers.