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Hazardous material (Hazmat) transportation is an inseparable section of the industry, despite its major financial and health risks. In order to optimize Hazmat transportation, a multi-objective Hazmat routing model with time windows is employed where the risk and distance are minimized. Due to the uncertainty of Hazmat transportation risk, a Z-number fuzzy approach is used to estimate the risk, in which the probability of occurrence and the severity is considered in the context of Z-information. The severity of the event includes the affected population and depends on the amount of transported Hazmat and the number of individuals affected by the explosion. To tackle the proposed model, the present paper utilizes a multi-objective hybrid genetic algorithm, the validity of which is tested by Solomon's problems. Furthermore, the optimization of a case study concerning the Hazmat distribution in Iran is analyzed using the suggested approach to assess the efficiency of the proposed fuzzy problem in real-world applications.