The assessment of the health status of healthcare workers (HWs) is related to the growing interest in the sustainability of the medical profession. This study explores for the first time the level of burnout, coping strategies, and pulse wave velocity (PWV), the correlations between them, and possible connections with the workplace. It included 154 HWs, aged 25–64 years, 83.76% women, divided into five groups (oncology, cardiology, intensive care, occupational health, and residents). The Burnout Assessment Tool (BAT-23) questionnaire for the burnout level and the Carver Coping Orientation to Problems Experienced (COPE) questionnaire for the coping strategies were used. PWV was measured with a TensioMed arteriograph. Regarding BAT subscales, all studied groups are at burnout for exhaustion (E), prone to burnout for mental distancing (MD), emotional impairment (EI), and no burnout for cognitive impairment (CI). On the four subscales of the BAT, the MANOVA shows a medium-sized effect of the workplace on MD and on CI. All subjects use positive coping strategies. Problem-solving mechanisms are often used, followed by emotional support-based and social support-based coping. PWV correlates with age and BMI and has a small positive correlation with MD, CI, and EI. High burnout levels are related to the healthcare profession, not to the workplace. Our research shows the practical need to supervise the mental and physical health of HWs in order to preserve their health through medical and organizational methods.