Blood cancer, or leukemia, has a negative impact on the blood and/or bone marrow of children and adults. Acute lymphocytic leukemia (ALL) and acute myeloid leukemia (AML) are two sub-types of acute leukemia. The Internet of Medical Things (IoMT) and artificial intelligence have allowed for the development of advanced technologies to assist in recently introduced medical procedures. Hence, in this paper, we propose a new intelligent IoMT framework for the automated classification of acute leukemias using microscopic blood images. The workflow of our proposed framework includes three main stages, as follows. First, blood samples are collected by wireless digital microscopy and sent to a cloud server. Second, the cloud server carries out automatic identification of the blood conditions-either leukemias or healthy-utilizing our developed generative adversarial network (GAN) classifier. Finally, the classification results are sent to a hematologist for medical approval. The developed GAN classifier was successfully evaluated on two public data sets: ALL-IDB and ASH image bank. It achieved the best accuracy scores of 98.67% for binary classification (ALL or healthy) and 95.5% for multi-class classification (ALL, AML, and normal blood cells), when compared with existing state-of-the-art methods. The results of this study demonstrate the feasibility of our proposed IoMT framework for automated diagnosis of acute leukemia tests. Clinical realization of this blood diagnosis system is our future work.