COVID-19-like pandemics are a major threat to the global health system have the potential to cause high mortality across age groups. The advance of the Internet of Medical Things (IoMT) technologies paves the way toward developing reliable solutions to combat these pandemics. Medical images (i.e., X-rays, computed tomography (CT)) provide an efficient tool for disease detection and diagnosis. The cost, time, and efforts for acquiring and annotating, for instance, large CT datasets make it complicated to obtain large numbers of samples from a single institution. However, owing to the necessity to preserve the privacy of patient data, it is challenging to build a centralized dataset from many institutions, especially during a pandemic. Moreover, heterogeneity between institutions presents a barrier to building efficient screening solutions. Thus, this paper presents a fog-based federated generative domain adaption framework (FGDA), where fog nodes aggregate patients’ data necessary to collaboratively train local deep-learning models for disease screening in medical images from different institutions. Local differential privacy is presented to protect the local gradients against attackers during the global model aggregation. In FGDA, the generative domain adaptation (DA) method is introduced to handle data discrepancies. Experimental evaluation on a case study of COVID-19 segmentation demonstrated the efficiency of FGDA over competing learning approaches with statistical significance.