For the last few years, computer-aided diagnosis (CAD) has been increasing rapidly. Numerous machine learning algorithms have been developed to identify different diseases, e.g., leukemia. Leukemia is a white blood cells- (WBC-) related illness affecting the bone marrow and/or blood. A quick, safe, and accurate early-stage diagnosis of leukemia plays a key role in curing and saving patients' lives. Based on developments, leukemia consists of two primary forms, i.e., acute and chronic leukemia. Each form can be subcategorized as myeloid and lymphoid. There are, therefore, four leukemia subtypes. Various approaches have been developed to identify leukemia with respect to its subtypes. However, in terms of effectiveness, learning process, and performance, these methods require improvements. This study provides an Internet of Medical Things- (IoMT-) based framework to enhance and provide a quick and safe identification of leukemia. In the proposed IoMT system, with the help of cloud computing, clinical gadgets are linked to network resources. The system allows real-time coordination for testing, diagnosis, and treatment of leukemia among patients and healthcare professionals, which may save both time and efforts of patients and clinicians. Moreover, the presented framework is also helpful for resolving the problems of patients with critical condition in pandemics such as COVID-19. The methods used for the identification of leukemia subtypes in the suggested framework are Dense Convolutional Neural Network (DenseNet-121) and Residual Convolutional Neural Network (ResNet-34). Two publicly available datasets for leukemia, i.e., ALL-IDB and ASH image bank, are used in this study. The results demonstrated that the suggested models supersede the other well-known machine learning algorithms used for healthy-versus-leukemia-subtypes identification.