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Deep neural network-based medical image classifications often use "hard" labels for training, where the probability of the correct category is 1 and those of others are 0. However, these hard targets can drive the networks over-confident about their predictions and prone to overfit the training data, affecting model generalization and adaption. Studies have shown that label smoothing and softening can improve classification performance. Nevertheless, existing approaches are either non-data-driven or limited in applicability. In this paper, we present the Class-Correlation Learning Network (CCL-Net) to learn interclass visual correlations from given training data, and produce soft labels to help with classification tasks. Instead of letting the network directly learn the desired correlations, we propose to learn them implicitly via distance metric learning of class-specific embeddings with a lightweight plugin CCL block. An intuitive loss based on a geometrical explanation of correlation is designed for bolstering learning of the interclass correlations. We further present end-to-end training of the proposed CCL block as a plugin head together with the classification backbone while generating soft labels on the fly. Our experimental results on the International Skin Imaging Collaboration 2018 dataset demonstrate effective learning of the interclass correlations from training data, as well as consistent improvements in performance upon several widely used modern network structures with the CCL block.