The COVID-19 pandemic caused impact on public health worldwide. Brazil gained prominence during the pandemic due to the magnitude of disease. This study aimed to evaluate the spatial–temporal dynamics of incidence, mortality, and case fatality of COVID-19 and its associations with social determinants in Brazilian municipalities and epidemiological week. We modeled incidence, mortality, and case fatality rates using spatial–temporal Bayesian model. “Bolsa Família Programme” (BOLSAFAM) and “proportional mortality ratio” (PMR) were inversely associated with the standardized incidence ratio (SIR), while “health insurance coverage” (HEALTHINSUR) and “Gini index” were directly associated with the SIR. BOLSAFAM and PMR were inversely associated with the standardized mortality ratio (SMR) and standardized case fatality ratio (SCFR). The highest proportion of excess risk for SIR and the SMR started in the North, expanding to the Midwest, Southeast, and South regions. The highest proportion of excess risk for the SCFR outcome was observed in some municipalities in the North region and in the other Brazilian regions. The COVID-19 incidence and mortality in municipalities that most benefited from the cash transfer programme and with better social development decreased. The municipalities with a higher proportion of non-whites had a higher risk of becoming ill and dying from the disease.