Due to inter-class homogeneity and intra-class variability, the classification of skin lesions in dermoscopy images has remained difficult. Although deep convolutional neural networks (DCNNs) have achieved satisfactory performance for binary skin cancer classification, multiclass skin lesion classification is still an open problem due to the limited training samples and class imbalance issues. To tackle these issues, in this article, we propose a multi-CNN ensemble approach dubbed ${\mathrm{M}}^2\mathrm{CE}$ for multiclass skin lesion classification. The ${\mathrm{M}}^2\mathrm{CE}$ includes three individual CNN models, each helping in extracting different high-level features from skin images and thereby yielding different prediction results. First, we design a lightweight CNN model to extract prominent features and train it from scratch, which primarily aims at avoiding the data scarcity problem. Then, we ensemble two different pre-trained CNN models with the lightweight model to improve the performance and generalization capability. The proposed ensemble approach can effectively fuse the predictions of each individual CNN model using the averaging method. The ${\mathrm{M}}^2\mathrm{CE}$ approach is validated using a benchmark data set, HAM10000, which contains skin lesion images of seven different classes. The results demonstrate that the ${\mathrm{M}}^2\mathrm{CE}$ outperforms base CNN models and state-of-the-art approaches without using any external data.