Responsible use of social media requires a level of culture and awareness on the part of the user themselves that allows them to understand and absorb the enormous amount of information they receive through these mediums, verify it, and then share it with their friends and users. This leads to numerous problems related to public health and safety. This research aims to identify the most significant effects of the dissemination of fake news in times of crisis on public health and safety, as well as to propose strategies to overcome this phenomenon. A hybrid Grey-ARAS (Additive Ratio Assessment) model was used to rank the potential impacts and propose strategies to overcome them. Four experts in the field of public health, data analysis, and contagious diseases participated in this study to determine the weights. Eight factors affecting public health and safety were proposed, along with seven strategies to mitigate these impacts. The results showed that the most important factors are creating panic and anxiety among people along with the contribution to the misleading public policy decisions. The results also showed that the most appropriate strategies to overcome the impact of fake news are to encourage people to check facts and monitor social media. A sensitivity analysis of the results obtained was also performed, proposing 20 different scenarios to adjust the relative weights of the criteria. The results showed a certain stability when using different scenarios.