Psychological distress, an emotional condition with symptoms of anxiety and depression, leads to impaired function, behavior, and personal traits. The current study examined the association between social determinants of health and the severity of psychological distress among adults in the United States after the COVID-19 pandemic. Using multinomial multivariable logistic regression, we analyzed data from 5106 (n = 5106) participants in the Health Information National Trends Survey (HINTS) 6. Compared to non-Hispanic Whites, African Americans (AOR = 0.62, CI = 0.42–0.93) had lower odds of reporting mild psychological distress rather than no stress. Other variables associated with a higher likelihood of reporting moderate to severe psychological distress, rather than no distress, are being in the 50–64 years age group (AOR = 2.77, CI = 1.45–5.28), divorced (AOR = 2.50, CI = 1.70–3.69), and widowed (AOR = 3.78, CI = 2.15–6.64). Respondents living in an urban area had lower odds of reporting moderate to severe psychological distress (AOR = 0.56, CI = 0.39–0.80) compared to those living in rural areas. Our findings identify several risk factors for psychological distress by sociodemographic characteristics such as age, race, marital status, and urban living, providing empirical evidence for interventions in behavioral health. These findings suggest there is an utmost need for a multi-sectoral approach to address the social determinants of health associated with psychological distress post-COVID-19 pandemic.