Deep learning approaches play a crucial role in computer-aided diagnosis systems to support clinical decision-making. However, developing such automated solutions is challenging due to the limited availability of annotated medical data. In this study, we proposed a novel and computationally efficient deep learning approach to leverage small data for learning generalizable and domain invariant representations in different medical imaging applications such as malaria, diabetic retinopathy, and tuberculosis. We refer to our approach as Incremental Modular Network Synthesis (IMNS), and the resulting CNNs as Incremental Modular Networks (IMNets). Our IMNS approach is to use small network modules that we call SubNets which are capable of generating salient features for a particular problem. Then, we build up ever larger and more powerful networks by combining these SubNets in different configurations. At each stage, only one new SubNet module undergoes learning updates. This reduces the computational resource requirements for training and aids in network optimization. We compare IMNets against classic and state-of-the-art deep learning architectures such as AlexNet, ResNet-50, Inception v3, DenseNet-201, and NasNet for the various experiments conducted in this study. Our proposed IMNS design leads to high average classification accuracies of 97.0%, 97.9%, and 88.6% for malaria, diabetic retinopathy, and tuberculosis, respectively. Our modular design for deep learning achieves the state-of-the-art performance in the scenarios tested. The IMNets produced here have a relatively low computational complexity compared to traditional deep learning architectures. The largest IMNet tested here has 0.95 M of the learnable parameters and 0.08 G of the floating-point multiply–add (MAdd) operations. The simpler IMNets train faster, have lower memory requirements, and process images faster than the benchmark methods tested.