Food insecurity is a major public health challenge that is associated with negative health outcomes in wealthy countries. In US urban areas, food banks and pantries played an expanded role in providing emergency food assistance and addressing food insecurity during the COVID-19 pandemic. This study seeks to determine if socially vulnerable neighborhoods are more likely to receive emergency food assistance during this pandemic, after controlling for distance to emergency food distribution sites and spatial clustering. The study area is El Paso County, Texas—an urban area on the US-Mexico border. Dependent variables represent both coverage and intensity of emergency food transfers (EFTs) from local food banks and pantries during November 2020, at the census tract level. Independent variables are derived from the widely used Social Vulnerability Index (SVI) developed by the Centers for Disease Control and Prevention and Agency for Toxic Substances and Disease Registry. Our statistical analyses are based on multivariable generalized estimating equations that account for spatial clustering and proximity to emergency food distribution sites. Results indicate that both coverage and intensity of EFTs are significantly greater in neighborhoods with higher social vulnerability and proximity to emergency food distribution sites, but lower in neighborhoods that are more vulnerable in terms of housing and transportation. Our findings highlight the significance of neighborhood-level social factors in influencing access to the emergency food network during a public health crisis and have important implications for government agencies and nonprofit organizations associated with public health and emergency preparedness in US urban areas.