The emergence of the Internet of Things (IoT) in the medical field has led to the massive deployment of a myriad of medical connected objects (MCOs). These MCOs are being developed and implemented for remote healthcare monitoring purposes including elderly patients with chronic diseases, pregnant women, and patients with disabilities. Accordingly, different associated challenges are emerging and include the heterogeneity of the gathered health data from these MCOs with ever‐changing contexts. These contexts are relative to the continuous change of constraints and requirements of the MCOs deployment (time, location, state). Other contexts are related to the patient (medical record, state, age, sex, etc.) that should be taken into account to ensure a more precise and appropriate treatment of the patient. These challenges are difficult to address due to the absence of a reference model for describing the health data and their sources and linking these data with their contexts. This article addresses this problem and introduces a semantic‐based context‐aware system (IoT Medicare system) for patient monitoring with MCOs. This system is based on a core domain ontology (HealthIoT‐O), that is, designed to describe the semantic of heterogeneous MCOs and their data. Moreover, an efficient interpretation and management of this knowledge in diverse contexts are ensured through SWRL rules such as the verification of the proper functioning of the MCOs and the analysis of the health data for diagnosis and treatment purposes. A case study of gestational diabetes disease management is proposed to evaluate the effectiveness of the implemented IoT Medicare system. An evaluation phase is provided and focuses on the quality of the elaborated semantic model and the performance of the system.