As modern complex neural networks keep breaking records and solving harder problems, their predictions also become less and less intelligible. The current lack of interpretability often undermines the deployment of accurate machine learning tools in sensitive settings. In this work, we present a model-agnostic explanation method for image classification based on a hierarchical extension of Shapley coefficients–Hierarchical Shap (h-Shap)–that resolves some of the limitations of current approaches. Unlike other Shapley-based explanation methods, h-Shap is scalable and can be computed without the need of approximation. Under certain distributional assumptions, such as those common in multiple instance learning, h-Shap retrieves the exact Shapley coefficients with an exponential improvement in computational complexity. We compare our hierarchical approach with popular Shapley-based and non-Shapley-based methods on a synthetic dataset, a medical imaging scenario, and a general computer vision problem, showing that h-Shap outperforms the state of the art in both accuracy and runtime. Code and experiments are made publicly available.