Background: The COVID-19 pandemic resulted in unprecedented restrictions on public and private life. The aim of the study was to investigate the impact of the COVID-19 pandemic on the physical and mental health of employees in the public sector, especially patient-related professions. Methods: For the data collection in summer 2021, an online questionnaire was used. Compared to a pre-pandemic point of time, the prevalence, frequency, and intensity of musculoskeletal pain, mental well-being, health status, and quality of life were recorded. Results: The questionnaire was completed by 1678 employees (f: 1045, m: 617). A total of 1504 employees (89.6%) were affected by complaints. Compared to before the pandemic, the prevalence and intensity of musculoskeletal complaints and psychological distress increased significantly. Patient-related professions (n = 204) showed significantly higher levels of stress and discomfort in several aspects (p < 0.05). Conclusions: Due to the COVID-19 pandemic, there was an increase in musculoskeletal complaints and a decrease in psychological well-being. Preventive factors related to mental health were identified as male gender, a middle- to older-age group, employees with children, and working from home. Attention should be drawn to these findings and prevention strategies should be brought into focus to strengthen the employees’ health. Special focus should be drawn to patient-related professions who are particularly confronted with pandemic-associated challenges.