To analyze the relationships between sociodemographic variables, intolerance to uncertainty (INT), social support, and psychological distress (i.e., indicators of Common Mental Disorders (CMDs) and perceived stress (PS)) in Brazilian men during the COVID-19 pandemic. A cross-sectional study with national coverage, of the web survey type, and conducted with 1006 Brazilian men during the period of social circulation restriction imposed by the health authorities in Brazil for suppression of the coronavirus and control of the pandemic. Structural equation modeling analysis was performed. Statistically significant direct effects of race/skin color (λ = 0.268; p-value < 0.001), socioeconomic status (SES) (λ = 0.306; p-value < 0.001), household composition (λ = 0.281; p-value < 0.001), PS (λ = 0.513; p-value < 0.001), and INT (λ = 0.421; p-value < 0.001) were evidenced in the occurrence of CMDs. Black-skinned men with higher SES, living alone, and with higher PS and INT levels presented higher prevalence values of CMDs. High levels of PS and INT were the factors that presented the strongest associations with the occurrence of CMDs among the men. It is necessary to implement actions to reduce the stress-generating sources as well as to promote an increase in resilience and the development of intrinsic reinforcements to deal with uncertain threats.