Training deep Convolutional Neural Networks (CNNs) presents challenges in terms of memory requirements and computational resources, often resulting in issues such as model overfitting and lack of generalization. These challenges can only be mitigated by using an excessive number of training images. However, medical image datasets commonly suffer from data scarcity due to the complexities involved in their acquisition, preparation, and curation. To address this issue, we propose a compact and hybrid machine learning architecture based on the Morphological and Convolutional Neural Network (MCNN), followed by a Random Forest classifier. Unlike deep CNN architectures, the MCNN was specifically designed to achieve effective performance with medical image datasets limited to a few hundred samples. It incorporates various morphological operations into a single layer and uses independent neural networks to extract information from each signal channel. The final classification is obtained by utilizing a Random Forest classifier on the outputs of the last neural network layer. We compare the classification performance of our proposed method with three popular deep CNN architectures (ResNet-18, ShuffleNet-V2, and MobileNet-V2) using two training approaches: full training and transfer learning. The evaluation was conducted on two distinct medical image datasets: the ISIC dataset for melanoma classification and the ORIGA dataset for glaucoma classification. Results demonstrate that the MCNN method exhibits reliable performance in melanoma classification, achieving an AUC of 0.94 (95% CI: 0.91 to 0.97), outperforming the popular CNN architectures. For the glaucoma dataset, the MCNN achieved an AUC of 0.65 (95% CI: 0.53 to 0.74), which was similar to the performance of the popular CNN architectures. This study contributes to the understanding of mathematical morphology in shallow neural networks for medical image classification and highlights the potential of hybrid architectures in effectively learning from medical image datasets that are limited by a small number of case samples.