Residents of Puerto Rico bear a significant burden of mental health disorders, which the COVID-19 pandemic may have exacerbated. However, age-specific data on these disorders during the pandemic in Puerto Rico are scarce. This study evaluated age-related differences in the self-reported diagnosis of depression and anxiety among adults ≥18 years residing in Puerto Rico during the pandemic. An anonymous online survey was administered from December 2020 to February 2021 via Google Forms to measure self-reported sociodemographic and behavioral characteristics and physician-diagnosed mental health disorders. Multivariable logistic regression models were conducted for each self-reported mental health diagnosis after adjusting for sex, education, income, marital status, chronic diseases, and smoking. Out of 1945 adults, 50% were aged 40 years and over. Nearly 24% of responders self-reported an anxiety diagnosis, whereas 15.9% reported depression. Compared to individuals 50 years and over, those 18–29 y, 30–39 y, and 40–49 y had significantly higher odds of an anxiety diagnosis (OR = 1.84, 95% CI = 1.34–2.55; OR = 1.50, 95% CI = 1.09–2.07; and OR = 1.37, 95% CI = 1.01–1.87, respectively). However, no association between age and depression diagnosis was found. Despite anxiety and depression being frequent disorders during the pandemic in this sample, younger adults bear a higher burden of anxiety. Further research is needed to allocate appropriate mental health resources during emergencies according to population subgroups.