Objectives: The aim of this ecological study was to investigate what the impact of digital learning due to the COVID-19 pandemic was on the burnout and overall mental health (MH) of medical students. Background: During the unprecedented era of the COVID-19 pandemic, the majority of countries worldwide adopted very strong measures. Universities closed their doors, and education continued through digital learning lectures. Methods: An anonymous questionnaire was administered to all 189 eligible candidates before and during the COVID-19 pandemic. Mental health was assessed via the MH domain of the 36-item Short Form Health Survey (SF-36) and burnout with the Maslach Burnout Inventory—Student Survey (MBI-SS). Results: The overall response rate was 81.5%. The overall burnout prevalence did not differ significantly between the two periods (pre-COVID-19 18.1% vs. COVID-19 18.2%). However, the burnout prevalence dropped significantly in year 4 (pre-COVID-19 40.7% vs. COVID-19 16.7%, p = 0.011), whereas it increased significantly in year 6 (pre-COVID-19 27.6% vs. COVID-19 50%, p = 0.01). When looking at each MBI-SS dimension separately, we found that emotional exhaustion decreased significantly in year 4 but increased in year 6, and cynicism increased in all years. The overall MH deteriorated significantly between the two periods (pre-COVID-19 58.8 ± 21.6 vs. COVID-19 48.3 ± 23, p < 0.001). Conclusions: Digital learning in medical studies carries significant risks. Not only does the MH deteriorate, but cynicism levels also increase. Emotional exhaustion was found to increase particularly in final year students, who struggle with the lack of clinical experience just before they start working as qualified junior doctors.