We investigated whether anxiety sensitivity (AS) is associated with increased distress and adherence to public health guidelines during the COVID-19 pandemic among undergraduates, and whether increased distress mediates the relationship between AS and increased adherence. An online cross-sectional survey was conducted with 1318 first- and second-year undergraduates (mean age of 19.2 years; 79.5% females) from five Canadian universities. Relevant subscales of the Substance Use Risk Profile Scale (SURPS) and the Big Five Inventory-10 (BFI-10) were used to assess AS and neuroticism. Three measures tapped distress: the Patient Health Questionnaire-9 (PHQ-9) for depressive symptoms, the Generalized Anxiety Disorder-7 (GAD-7) for anxiety symptoms, and the Brief COVID-19 Stress Scales (CSS-B) for COVID-19-specific distress. The COVID-19 Adherence scale (CAD) assessed adherence to COVID-19 containment measures. AS was significantly independently associated with higher general distress (both anxiety and depressive symptoms) and higher COVID-19-specific distress, after controlling age, sex, study site, and neuroticism. Moreover, AS indirectly predicted greater adherence to COVID-19 preventive measures through higher COVID-19-specific distress. Interventions targeting higher AS might be helpful for decreasing both general and COVID-19-specific distress, whereas interventions targeting lower AS might be helpful for increasing adherence to public health containment strategies, in undergraduates.