The deadly coronavirus disease (COVID-19) has highlighted the importance of remote health monitoring (RHM). The digital twins (DTs) paradigm enables RHM by creating a virtual replica that receives data from the physical asset, representing its real-world behavior. However, DTs use passive internet of things (IoT) sensors, which limit their potential to a specific location or entity. This problem can be addressed by using the internet of robotic things (IoRT), which combines robotics and IoT, allowing the robotic things (RTs) to navigate in a particular environment and connect to IoT devices in the vicinity. Implementing DTs in IoRT, creates a virtual replica (virtual twin) that receives real-time data from the physical RT (physical twin) to mirror its status. However, DTs require a user interface for real-time interaction and visualization. Virtual reality (VR) can be used as an interface due to its natural ability to visualize and interact with DTs. This research proposes a real-time system for RHM of COVID-19 patients using the DTs-based IoRT and VR-based user interface. It also presents and evaluates robot navigation performance, which is vital for remote monitoring. The virtual twin (VT) operates the physical twin (PT) in the real environment (RE), which collects data from the patient-mounted sensors and transmits it to the control service to visualize in VR for medical examination. The system prevents direct interaction of medical staff with contaminated patients, protecting them from infection and stress. The experimental results verify the monitoring data quality (accuracy, completeness, timeliness) and high accuracy of PT's navigation.