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 a weak binding energy that, 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 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.