Preventing burnout and promoting positive mental health among medical students is important. Relevant research is lacking on positive mental health in medical students, particularly in low- and middle-income countries. We conducted a cross-sectional survey of Sri Lankan students enrolled in a five-year medical program. Measures included the Mental Health Continuum-Short Form, Kessler 10 Psychological Distress Scale, and Oldenburg Burnout Inventory. We investigated relationships between year in program, mental health indicators, and academic performance. Three hundred twenty-seven students participated (35% response rate). Most students had moderate positive mental health (64.8%) and severe psychological distress (40.4%). Final year students reported more psychological distress and burnout than first year students. Female students had higher burnout scores than males. In multivariable models, fourth and fifth year students evidenced lower positive mental health than first year students. Mental health indicators were unassociated with academic performance. Overall, distress rates were higher than those reported among students in other countries. Higher burnout and distress may be driven by increased responsibilities in the final clinical years of training. Bolstering positive mental health through positive emotions, meaning, and social connection may minimize burnout and distress, although extracurricular activities require time. Interventions to reduce medical student distress in Sri Lanka are needed.