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Knowing when a machine learning system is not confident about its prediction is crucial in medical domains where safety is critical. Ideally, a machine learning algorithm should make a prediction only when it is highly certain about its competency, and refer the case to physicians otherwise. In this paper, we investigate how Bayesian deep learning can improve the performance of the machine–physician team in the skin lesion classification task. We used the publicly available HAM10000 dataset, which includes samples from seven common skin lesion categories: Melanoma (MEL), Melanocytic Nevi (NV), Basal Cell Carcinoma (BCC), Actinic Keratoses and Intraepithelial Carcinoma (AKIEC), Benign Keratosis (BKL), Dermatofibroma (DF), and Vascular (VASC) lesions. Our experimental results show that Bayesian deep networks can boost the diagnostic performance of the standard DenseNet-169 model from 81.35% to 83.59% without incurring additional parameters or heavy computation. More importantly, a hybrid physician–machine workflow reaches a classification accuracy of 90 % while only referring 35 % of the cases to physicians. The findings are expected to generalize to other medical diagnosis applications. We believe that the availability of risk-aware machine learning methods will enable a wider adoption of machine learning technology in clinical settings.