The COVID-19 pandemic has gravely impacted Latin America. A model was tested that evaluated the contribution of socio-demographic factors and fear of COVID-19 on anxiety and depression in samples of residents in seven Latin American countries (Argentina, Ecuador, Mexico, Paraguay, Uruguay, Colombia, and El Salvador). A total of 4,881 individuals, selected by convenience sampling, participated in the study. Moderate and severe levels of depressive symptoms and anxiety were identified, as well as a moderate average level of fear of COVID-19. In addition, it was observed that about a quarter of the participants presented symptoms of generalized anxiety disorder and a major depressive episode. Fear of COVID-19 significantly and positively predicted anxiety and depressive symptoms, whereas the effects of socio-demographic variables are generally low [χ2(287) = 5936.96, p < 0.001; RMSEA = 0.064 [0.062, 0.065]; CFI = 0.947; and SRMR = 0.050]. This suggests the need for the implementation of preventive actions in the general population of these countries, with the aim of reducing the prevalence of depressive, anxious and fearful symptoms related to COVID-19.