The recent global pandemic of the novel coronavirus disease 2019 (COVID-19) is affecting the entire population of Nepal, and the outcome of the epidemic varies from place to place. A district-level analysis was conducted to identify socio-demographic risk factors that drive the large variations in COVID-19 mortality and related health outcomes, as of 22 January 2021. Data on COVID-19 extracted from relevant reports and websites of the Ministry of Health and Population of Nepal, and the National Population and Housing Census and the Nepal Demographic and Health Survey were the main data sources for the district-level socio-demographic characteristics. We calculated the COVID-19 incidence, recovered cases, and deaths per 100,000 population, then estimated the associations with the risk factors using regression models. COVID-19 outcomes were positively associated with population density. A higher incidence of COVID-19 was associated with districts with a higher percentage of overcrowded households and without access to handwashing facilities. Adult literacy rate was negatively associated with the COVID-19 incidence. Increased mortality was significantly associated with a higher obesity prevalence in women and a higher smoking prevalence in men. Access to health care facilities reduced mortality. Population density was the most important driver behind the large variations in COVID-19 outcomes. This study identifies critical risk factors of COVID-19 outcomes, including population density, crowding, education, and hand hygiene, and these factors should be considered to address inequities in the burden of COVID-19 across districts.