Background Depression is a major morbidity and the most common mental disorder among the medical students in medical schools globally. Undergraduate students suffer stress more due to their academic curriculum than the students of other faculties. In low-resource settings like Bangladesh, there is a dearth in research on the mental health of undergraduate medical students. This pilot study was conducted to add to the existing limited evidence by reporting the prevalence of depression and describing sleeping pattern and suicidal tendencies among medical students. Relevantly, we have investigated the overall mental health status among the medical students in Bangladesh. Methods This cross-sectional study was conducted in two medical colleges of Dhaka between July 2013 and December 2013, among 221 Bangladeshi medical students from first to fifth year. By the convenience sampling technique, data were collected by a pretested, structured, self-administered questionnaire and analysis was done by SPSS version 18.0. Depression was assessed by the validated Patient Health Questionnaire-9 (PHQ-9) tool among the respondents. Goldberg's General Health Questionnaire (GHQ-28) was used for assessing overall mental health status. Results Depression was found in 38.9% of participants, with 3.6%, 14.5%, and 20.8% being severe, moderate, and mild depression, respectively. 17.6% of medical students had suicidal tendency or attempted suicide at least once after attending medical school. The sleeping hours were inadequate and altered after starting this stressful academic course. 33.5% of medical students had poor mental health status. There was a statistically significant association between poor mental health status in the age group less than 22 years old and initial academic study year (1st to 3rd of MBBS). Conclusion The findings are suggestive of a higher prevalence of depression among early-year medical students and marginal predominance in males. Suicidal tendency is also higher. This calls for further investigation with situation analysis, qualitative explorations, and surveys to explore the burden of such disorders in Bangladesh.