A few decades ago, robotics started to be implemented in the medical field, especially in the rehabilitation of patients with different neurological diseases that have led to neuromuscular disorders. The main concern regarding medical robots is their safety assurance in the medical environment. The goal of this paper is to assess the risk of a medical robotic system for elbow and wrist rehabilitation in terms of robot and patient safety. The approached risk assessment follows the ISO12100:2010 risk management chart in order to determine, identify, estimate, and evaluate the possible risk that can occur during the use of the robotic system. The result of the risk assessment process is further analyzed using a fuzzy logic system in order to determine the safety degree conferred during the use of the robotic system. The innovative process concerning the risk assessment allows the achievement of a reliable medical robotic system both for the patient and the clinicians as well. The clinical trials performed on a group of 18 patients validated the functionality and the safe behavior of the robotic system.