Mental health problems among undergraduate medical students is a well-known issue; however, their associated risk factors have been poorly studied. We aimed to assess the hypothesis that medical students have a higher prevalence of psychological distress and to explain this prevalence considering common risk factors for mental disorders. This was a cross-sectional, questionnaire-based descriptive study conducted with 467 Colombian undergraduate medical students from different years of training. Validated and widely used self-report questionnaires of psychological distress, daytime sleepiness, and family functioning were included. In addition, measurements of smoking, alcohol, and caffeine intake were used. We found a prevalence of psychological distress, depressive symptoms and anxiety symptomatology of 65.9%, 75.3%, and 50.5%, respectively. Furthermore, 20.6% showed both psychological distress and excessive daytime sleepiness. Adjusted risk ratio analysis showed that poor family functioning, the presence of excessive daytime sleepiness, and caffeine consumption were significant risk factors for high levels of psychological distress. Additionally, psychological distress and daytime sleepiness were related to the year of training. Our results replicate in part previous findings of poor mental health among undergraduate medical students compared with mental health in general population and provide novel findings that family functioning plays a significant role as an important explanatory factor. The current study has high relevance for future research and interventions focused on prevention of medical errors, conflicts in the physician–patient relationship and the personal safety of undergraduate medical students.