Early COVID-19 pandemic data suggested racial/ethnic minority and low-income earning people bore the greatest burden of infection. Structural racism, the reinforcement of racial and ethnic discrimination via policy, provides a framework for understanding disparities in health outcomes like COVID-19 infection. Residential racial and economic segregation is one indicator of structural racism. Little attention has been paid to the relationship of infection to relative overall concentrations of risk (i.e., segregation of the most privileged from the most disadvantaged). We used ordinary least squares and geographically weighted regression models to evaluate the relationship between racial and economic segregation, measured by the Index of Concentration at the Extremes, and COVID-19 cases in Louisiana. We found a significant global association between racial segregation and cumulative COVID-19 case rate in Louisiana and variation across the state during the study period. The northwest and central regions exhibited a strong negative relationship indicating greater risk in areas with high concentrations of Black residents. On the other hand, the southeastern part of the state exhibited more neutral or positive relationships indicating greater risk in areas with high concentrations of White residents. Our findings that the relationship between racial segregation and COVID-19 cases varied within a state further support evidence that social and political determinants, not biological, drive racial disparities. Small area measures and measures of polarization provide localized information better suited to tailoring public health policy according to the dynamics of communities at the census tract level, which may lead to better health outcomes.