Background Burnout is a state of emotional, mental, and physical exhaustion affecting a large number of health care workers. In Ethiopia, there is limited evidence about burnout syndrome and work-related determinant factors among health care workers. Therefore, this study aimed to determine the prevalence of burnout syndrome and identify the associated risk factors among public hospitals health care workers in Addis Ababa, Ethiopia, 2019. Methods Institution-based cross-sectional study design was employed from March 10 to May 13, 2019. Stratified random sampling with simple random sampling techniques was used to select participants. The standardized Maslach Burnout Inventory-Human service survey questionnaire was used to collect the data. Five-hundred twenty-five workers completed and valid questionnaire were entered into Epi Info version 7 and exported to SPSS version 20 for further analysis. Logistic regression analysis was used to identify factors associated with burnout syndrome. The significant level was obtained at p-value ≤ 0.05. Result The overall prevalence of burnout syndrome among health care workers in this study was found to be 31.6% (n = 166) (95%CI: 27.8, 36). Moreover, 42% (n = 218) of respondents were highly emotionally exhausted. In addition, 43% (n = 224) and 45% (n = 234) of respondents experienced depersonalization and low personal achievement, respectively. Age (AOR = 0.4, 95%CI: 0.2, 0.9), long night shift work (AOR = 3.36, 95%CI: 1.83, 6.2), job satisfaction (AOR = 2.08 95%CI: 1.3, 3.3), and educational level (AOR = 6.33, 95%CI: 2.3–17.5) were factors significantly associated with burnout syndrome. Conclusion This study shows that a high proportion of health care workers suffer from burnout syndrome. Low education level, long night- and day-shift work, and job dissatisfaction are significant determinant factors of burnout syndrome. Therefore, interventions focusing on shift work management, establishing stress management programs, and improving interpersonal relationships and working conditions to increase job satisfaction among health care workers are essential to reduce the problem.