Abstract: A cross-sectional survey conducted between July and September 2020 and August and September 2021 estimated the prevalence and predictors of common mental disorders (CMDs) and post-traumatic stress disorder (PTSD) among healthcare workers (HCWs) at an infectious disease referral center during the COVID-19 pandemic. CMDs were assessed using the General Health Questionnaire (GHQ-12), and PTSD using the Impact of Event Scale-Revised (IES-R). Multivariate logistic regressions identified predictors of CMD and PTSD. The study included 371 HCWs in 2020 and 167 in 2021. The CMD prevalence was 34.3% (95% confidence interval (CI): 29.5–39.4) in 2020 and 30.5% (95% CI: 23.7–38.1) in 2021. The PTSD prevalence was 25.4% (95% CI: 21.0–30.2) in 2020 and 32.7% (95% CI: 25.6–40.5) in 2021. Factors increasing CMD odds included lower education (adjusted odds ratio (AOR) = 3.71, 95% CI: 1.60–8.61), lack of physical activity (AOR = 2.23, 95% CI: 1.33–3.73), and experiencing COVID-19 symptoms (AOR = 1.64, 95% CI: 1.02–2.64) in 2020; chronic diseases (AOR = 3.14, 95% CI: 1.34–7.35) and SARS-CoV-2 testing (AOR = 3.39, 95% CI: 1.13–10.17) raised CMD odds in 2021. Frontline HCWs had lower CMD odds in 2020 (AOR = 0.60, 95% CI: 0.36–1.00) and 2021 (AOR = 0.33, 95% CI: 0.14–0.75). PTSD was associated with having COVID-19 symptoms (AOR = 2.06, 95% CI: 1.23–3.45), living with high-risk individuals (AOR = 1.75, 95% CI: 1.03–2.95), and losing loved ones (AOR = 1.86, 95% CI: 1.09–3.17) in 2020. Chronic diseases increased PTSD odds in 2020 (AOR = 2.20, 95% CI: 1.25–3.86) and 2021 (AOR = 2.30, 95% CI: 1.03–5.13), while age decreased them in 2020 (AOR = 0.95, 95% CI: 0.93–0.98) and 2021 (AOR = 0.95, 95% CI: 0.91–0.99). Younger HCWs with chronic conditions living with high-risk individuals were particularly affected. These findings highlight the urgent need for targeted emotional support and stress management programs for HCWs.