Coronavirus disease 2019 (COVID-19) was confirmed in Brazil in February 2020. Since then, the disease has spread throughout the country, reaching the poorest areas. This study analyzes the relationship between COVID-19 and the population's living conditions. We aimed to identify social determinants related to the incidence, mortality, and case fatality rate of COVID-19 in Brazil, in 2020. This is an ecological study evaluating the relationship between COVID-19 incidence, mortality, and case fatality rates and 49 social indicators of human development and social vulnerability. For the analysis, bivariate spatial correlation and multivariate and spatial regression models (spatial lag model and spatial error models) were used, considering a 95% confidence interval and a significance level of 5%. A total of 44.8% of municipalities registered confirmed cases of COVID-19 and 14.7% had deaths. We observed that 56.2% of municipalities with confirmed cases had very low human development (COVID-19 incidence rate: 59.00/100 000; mortality rate: 36.75/1 000 000), and 52.8% had very high vulnerability (COVID-19 incidence rate: 41.68/100 000; mortality rate: 27.46/1 000 000). The regression model showed 17 indicators associated with transmission of COVID-19 in Brazil. Although COVID-19 first arrived in the most developed and least vulnerable municipalities in Brazil, it has already reached locations that are farther from large urban centers, whose populations are exposed to a context of intense social vulnerability. Based on these findings, it is necessary to adopt measures that take local social aspects into account in order to contain the pandemic.