Black, Hispanic, and Indigenous persons in the United States have an increased risk of SARS-CoV-2 infection and death from COVID-19, due to persistent social inequities. The magnitude of the disparity is unclear, however, because race/ethnicity information is often missing in surveillance data. In this study, we quantified the burden of SARS-CoV-2 infection, hospitalization, and case fatality rates in an urban county by racial/ethnic group using combined race/ethnicity imputation and quantitative bias-adjustment for misclassification. After bias-adjustment, the magnitude of the absolute racial/ethnic disparity, measured as the difference in infection rates between classified Black and Hispanic persons compared to classified White persons, increased 1.3-fold and 1.6-fold respectively. These results highlight that complete case analyses may underestimate absolute disparities in infection rates. Collecting race/ethnicity information at time of testing is optimal. However, when data are missing, combined imputation and bias-adjustment improves estimates of the racial/ethnic disparities in the COVID-19 burden.