Occupational health and safety (OHS) risk assessment studies have gained importance recently as a result of increasing occupational accidents and occupational diseases. The health sector has a greater risk than many sectors for occupational accidents and occupational diseases. Although the health sector is one of the priority sectors in Turkey, OHS practices have not been fully implemented in this field. For this reason, this study adopts a two-stage approach to assess the OHS risks in the health sector by combining the Fine-Kinney and multi-criteria hesitant fuzzy linguistic term set (HFLTS) methods. The proposed method was applied to the OHS risks in the operating room of a public hospital in Turkey. As a solution to the problem, first, the potential hazards and related risks in the operating room were determined by the experts. In this first stage, 44 hazards were determined from the opinions of experts and records of past incidents. Parameter weights were then determined using the multi-criteria HFLTS method. The multi-criteria HFLTS method was used to evaluate seven hazards to be categorized as substantial-risk or higher according to the Fine-Kinney method, taking into account parameter weights. Sensitivity analysis was then carried out. Finally, actions were taken to mitigate the risks.