The importance of risk assessment in the context of occupational health and safety by manufacturing operators strengthens their hands in solving the problems they may encounter in business processes related to health and safety. One of the most important phases of conducting an exhaustive occupational risk assessment is to analyze potential hazards and associated risks quantitatively. Since manufacturing is one of the industries that require workers to be highly exposed to work, creating a safer environment to reduce occupational injuries is an important task. This study proposes a novel fuzzy risk assessment approach developed by integrating Fermatean fuzzy sets (FFSs) and technique for order preference by similarity to ideal solution (TOPSIS) method for ranking potential hazards in manufacturing. FFSs are a new version of fuzzy set theory that covers the intuitionistic fuzzy sets and Pythagorean fuzzy sets. This version of the fuzzy set is crucial in the decision-making process to handle uncertain information more easily and reflect uncertainty better. A linguistic scale under Fermatean fuzzy documentation has also been developed for experts/decision makers to disclose their judgments easily. Occupational risk analysts can benefit from this approach since FFSs are used for the first time in occupational risk assessment, and the approach is presented in integration with TOPSIS. The proposed approach is applied in the aluminum plate-manufacturing process risk assessment. In the conclusion of the implementation, risks arising in the production are prioritized. In addition, this study made comparisons with other fuzzy methods to demonstrate the proposed approach’s difference and practicality. This study’s results can support practitioners and risk analysts in formulating the improvement measures to increase the safety of the work environment further.