The increasing application of artificial intelligence (AI) to healthcare raises both hope and ethical concerns. Some advanced machine learning methods provide accurate clinical predictions at the expense of a significant lack of explainability. Alex John London has defended that accuracy is a more important value than explainability in AI medicine. In this article, we locate the trade-off between accurate performance and explainable algorithms in the context of distributive justice. We acknowledge that accuracy is cardinal from outcome-oriented justice because it helps (...) to maximize patients’ benefits and optimizes limited resources. However, we claim that the opaqueness of the algorithmic black box and its absence of explainability threatens core commitments of procedural fairness such as accountability, avoidance of bias, and transparency. To illustrate this, we discuss liver transplantation as a case of critical medical resources in which the lack of explainability in AI-based allocation algorithms is procedurally unfair. Finally, we provide a number of ethical recommendations for when considering the use of unexplainable algorithms in the distribution of health-related resources. (shrink)