The COronaVIrus Disease 2019 (COVID-19) pandemic is unfortunately highly transmissible across the people. In order to detect and track the suspected COVID-19 infected people and consequently limit the pandemic spread, this paper entails a framework integrating the machine learning (ML), cloud, fog, and Internet of Things (IoT) technologies to propose a novel smart COVID-19 disease monitoring and prognosis system. The proposal leverages the IoT devices that collect streaming data from both medical (e.g., X-ray machine, lung ultrasound machine, etc.) and non-medical (e.g., bracelet, smartwatch, etc.) devices. Moreover, the proposed hybrid fog-cloud framework provides two kinds of federated ML as a service (federated MLaaS); (i) the distributed batch MLaaS that is implemented on the cloud environment for a long-term decision-making, and (ii) the distributed stream MLaaS, which is installed into a hybrid fog-cloud environment for a short-term decision-making. The stream MLaaS uses a shared federated prediction model stored into the cloud, whereas the real-time symptom data processing and COVID-19 prediction are done into the fog. The federated ML models are determined after evaluating a set of both batch and stream ML algorithms from the Python’s libraries. The evaluation considers both the quantitative (i.e., performance in terms of accuracy, precision, root mean squared error, and F1 score) and qualitative (i.e., quality of service in terms of server latency, response time, and network latency) metrics to assess these algorithms. This evaluation shows that the stream ML algorithms have the potential to be integrated into the COVID-19 prognosis allowing the early predictions of the suspected COVID-19 cases.