Background: Medical interns are at risk of burnout due to several organizational and individual factors. There is scarcity of studies exploring the role of chronic physical illness and job dissatisfaction on burnout experience among medical interns. This study examined the prevalence of burnout syndrome and explored whether chronic physical illness and job dissatisfaction could independently predict burnout syndrome among medical interns in Oman. This cross-sectional study was conducted among a random sample of medical interns enrolled in the Omani internship program. One-hundred and eighty interns participated in this study and filled in a self-reported questionnaire that included Maslach Burnout Inventory (MBI), Job Satisfaction Survey (JSS), and data related to physical illness. Results: The prevalence of burnout syndrome was 15%. Having a physical illness (OR = 7.285, 95% CI = 1.976–26.857, P = 0.003) and job dissatisfaction (OR = 16.488, 95% CI = 5.371–50.614, P = 0.0001) was significant independent predictors of high levels of the EE subscale. In addition, having a physical illness (OR = 4.678, 95% CI = 1.498–14.608, P = 0.008) and being dissatisfied (OR = 2.900, 95% CI = 11.159–7.257, P = 0.023) were significant independent predictors of the high DP subscale. Having physical illness was independent predictors of the low personal accomplishment subscale (OR = 0.258, 95% CI = 0.088–0.759, P = 0.014). Conclusions: Burnout syndrome is prevalent among medical interns in Oman. Job dissatisfaction and chronic physical illness are risk factors for burnout syndrome. Internship programs should consider these factors when designing burnout mitigative strategies.