This study aimed to analyse the geographical distribution of coronavirus disease 2019 (COVID-19) and to identify high-risk areas in space and time for the occurrence of cases and deaths in the indigenous population of Brazil. This is an ecological study carried out between 24 March and 26 October 2020 whose units of analysis were the Special Indigenous Sanitary Districts. The Getis-Ord General G and Getis-Ord Gi* techniques were used to verify the spatial association of the phenomena and a retrospective space–time scan was performed. There were 32 041 confirmed cases of COVID-19 and 471 deaths. The non-randomness of cases (z score = 5.40; P < 0.001) and deaths (z score = 3.83; P < 0.001) were confirmed. Hotspots were identified for cases and deaths in the north and midwest regions of Brazil. Sixteen high-risk space–time clusters were identified for the occurrence of cases with a higher RR = 21.23 (P < 0.001) and four risk clusters for deaths with a higher RR = 80.33 (P < 0.001). These clusters were identified from 22 May and were active until 10 October 2020. The results indicate critical areas in the indigenous territories of Brazil and contribute to better directing the actions of control of COVID-19 in this population.