COVID-19 is an infectious disease caused by the recently discovered coronavirus SARS-Cov-2. The disease became pandemic affecting many countries globally, including Brazil. Considering the expansion process and particularities during the initial stages of the epidemic, we aimed to analyze the spatial and spatiotemporal patterns of COVID-19 occurrence and to identify priority risk areas in Minas Gerais State, Southeast Brazil. An ecological study was performed considering all data from human cases of COVID-19 confirmed from the epidemiological week (EW) 11 (March 08, 2020) to EW 26 (June 27, 2020). Crude and smoothed incidence rates were used to analyze the distribution of disease patterns based on global and local indicators of spatial association and space-time risk assessment. Positive spatial autocorrelation and spatial dependence were found. Our results suggest that the metropolitan region of the State capital Belo Horizonte (MRBH) and Vale do Rio Doce mesoregions, as major epidemic foci in the beginning of the expansion process, have had important influence on the dispersion of SARS-CoV-2 in Minas Gerais State. Triangulo Mineiro/Alto Paranaiba region presented the highest risk of infection. In addition, six statistically significant spatiotemporal clusters were identified in the State, three at high risk and three at low risk. Our findings contribute to a greater understanding of the space-time disease dynamic and discuss strategies for identification of priority areas for COVID-19 surveillance and control.