Background: A healthcare system’s collapse due to a pandemic, such as the coronavirus disease 2019 (COVID-19), can expose healthcare workers (HCWs) to various mental health problems. This study aimed to investigate the impact of the COVID-19 pandemic on the depression and anxiety of HCWs. Methods: A nationwide questionnaire-based survey was conducted on HCWs who worked in healthcare facilities and public health centers in Korea in December 2020. Patient Health Questionnaire-9 (PHQ-9) and Generalized Anxiety Disorder-7 (GAD-7) were used to measure depression and anxiety. To investigate factors associated with depression and anxiety, stepwise multiple logistic regression analysis was performed. Results: A total of 1,425 participating HCWs were included. The mean depression score (PHQ-9) of HCWs before and after COVID-19 increased from 2.37 to 5.39, and the mean anxiety score (GAD-7) increased from 1.41 to 3.41. The proportion of HCWs with moderate to severe depression (PHQ-9 ≥ 10) increased from 3.8% before COVID-19 to 19.5% after COVID-19, whereas that of HCWs with moderate to severe anxiety (GAD-7 ≥ 10) increased from 2.0% to 10.1%. In our study, insomnia, chronic fatigue symptoms and physical symptoms after COVID-19, anxiety score (GAD-7) after COVID-19, living alone, and exhaustion were positively correlated with depression. Furthermore, post-traumatic stress symptoms, stress score (Global Assessment of Recent Stress), depression score (PHQ-9) after COVID-19, and exhaustion were positively correlated with anxiety. Conclusion In Korea, during the COVID-19 pandemic, HCWs commonly suffered from mental health problems, including depression and anxiety. Regularly checking the physical and mental health problems of HCWs during the COVID-19 pandemic is crucial, and social support and strategy are needed to reduce the heavy workload and psychological distress of HCWs.