As global deaths from COVID-19 continue to rise, the world's governments, institutions, and agencies are still working toward an understanding of who is most at risk of death. In this study, data on all recorded COVID-19 deaths in Sweden up to May 7, 2020 are linked to high-quality and accurate individual-level background data from administrative registers of the total population. By means of individual-level survival analysis we demonstrate that being male, having less individual income, lower education, not being married all independently predict a higher risk of death from COVID-19 and from all other causes of death. Being an immigrant from a low- or middle-income country predicts higher risk of death from COVID-19 but not for all other causes of death. The main message of this work is that the interaction of the virus causing COVID-19 and its social environment exerts an unequal burden on the most disadvantaged members of society.