The determinants of severe COVID-19 in healthy adults are poorly understood, which limits the opportunity for early intervention. We present a multiomic analysis using machine learning to characterize the genomic basis of COVID-19 severity. We use single-cell multiome profiling of human lungs to link genetic signals to cell-type-specific functions. We discover >1,000 risk genes across 19 cell types, which account for 77% of the SNP-based heritability for severe disease. Genetic risk is particularly focused within natural killer (NK) cells and T cells, placing the dysfunction of these cells upstream of severe disease. Mendelian randomization and single-cell profiling of human NK cells support the role of NK cells and further localize genetic risk to CD56bright NK cells, which are key cytokine producers during the innate immune response. Rare variant analysis confirms the enrichment of severe-disease-associated genetic variation within NK-cell risk genes. Our study provides insights into the pathogenesis of severe COVID-19 with potential therapeutic targets.