Occupational stress and burnout are a global epidemic that can cause severe negative effects on workers’ physical and emotional health. Health professionals working in a hospital setting are especially at risk, due to the inherent characteristics of their work. Consequently, this study aimed to analyse the relationships between stress and burnout in health professionals working in a hospital in the North of Portugal. A convenience sample of 221 health professionals participated in this cross-sectional study and answered two instruments to assess stress and burnout at work. Results showed that stress dimensions, such as the precariousness of the contractual status, the intention to change services, work overload, stress from the work-home interface, relationships at work, leading training activities, and dealing with patients predicted the three dimensions of burnout—physical fatigue, cognitive weariness, and emotional exhaustion. Therefore, these findings contribute to increase the knowledge of health professional’s mental conditions, and can be used to design and implement interventions to mitigate the effects of stress and burnout on these professionals.