We examine the uneven social and spatial distributions of COVID-19 and their relationships with indicators of social vulnerability in the U.S. epicenter, New York City (NYC). As of July 17th, 2020, NYC, despite having only 2.5% of the US population, has ~6% of all confirmed cases, and ~16% of all deaths, making it a key learning ground for the social dynamics of the disease. Our analysis focuses on the multiple potential social, economic, and demographic drivers of disproportionate impacts in COVID-19 cases and deaths, as well as population rates of testing. Findings show that immediate impacts of COVID-19 largely fall along lines of race and class. Indicators of poverty, race, disability, language isolation, rent burden, unemployment, lack of health insurance, and housing crowding all significantly drive spatial patterns in prevalence of COVID-19 testing, confirmed cases, death rates, and severity. Income in particular has a consistent negative relationship with rates of death and disease severity. The largest differences in social vulnerability indicators are also driven by populations of people of color, poverty, housing crowding, and rates of disability. Results highlight the need for targeted responses to address injustice of COVID-19 cases and deaths, importance of recovery strategies that account for differential vulnerability, and provide an analytical approach for advancing research to examine potential similar injustice of COVID-19 in other U.S. cities.