During the COVID-19 pandemic, fake news proliferated along with the concern that they would affect behavior regarding the disease. With a semi-representative survey in Mexico (N = 1211), this study analyzes a mediational process to determine the impact of the use of traditional and social media on compliance with contagion prevention measures, through the perception of veracity of fake news about COVID-19. As anticipated, results indicate that believing fake news leads to less compliance of preventive measures. Likewise, the analysis indicates that, consistent with our hypothesis, using social media leads to more belief in fake news, but contrary to our expectations, consuming traditional media also leads to a greater belief in fake news. In particular, the study explored the mediating role of belief in fake news on the effect that using traditional and social media has on compliance with preventive measures. We found evidence for this indirect effect: use of traditional and social media is a predictor of believing fake news about COVID-19, which then results in lower compliance with measures. In contrast, the direct effect of using traditional and social media on compliance with measures has a positive direction. Thus, this work evinces that fake news can hinder the resolution of the health crisis, by discouraging compliance with preventive strategies.