Scientific experiments cover a wide range of fields—from basic to applied scientific research. Chemical experiments are the basis for cultivating chemical knowledge in scientific experiments and are an important way to cultivate scientific thinking and methods. However, due to the toxicity or flammability of the chemical substances in the experiments, hazardous events often lead to personal injuries and environmental damage. Exactly assessing risk factors and reducing the risk of hazards to protect the experimenters and ensure environmental safety are crucial in chemical experiments. However, while the traditional risk evaluation method cannot consider the weight of risk evaluation criteria, it also cannot effectively address problems through hierarchical analysis, as well as imprecise and ambiguous information inherent in human cognition. Therefore, this paper proposed an approach based on failure mode and effects analysis (FMEA) to assess the risk of chemical experiments in a fuzzy information environment. The approach combines the typical analytic hierarchy process (AHP), the risk priority number (RPN) of FMEA, and the intuitionistic fuzzy set (IFS) methods to evaluate risks associated with chemical experiments and consider the damage recovery in chemical experiments. This study applied the case of a university chemistry experiment, “preparation of hydrogels”, to validate the reasonableness and correctness of the proposed approach and compare its numerical verification results with those from the typical RPN, the AHP-RPN, and the AHP-fuzzy risk priority number (AHP-FRPN) methods. The finding demonstrates that the proposed method can more effectively address risk evaluation problems in chemical experiments than the other methods. This result serves as an important reference for reducing chemical experiment risk occurrences.