Negative attitudes toward mental illness and treatment are attributed to a lack of or inaccurate mental health knowledge. We aimed to assess the current mental health knowledge and awareness among Bangladeshi university students and identified socio-demographic factors that affect them. Between February and April of 2021, a cross-sectional study of 2036 university students in Bangladesh was conducted. Two different questionnaires (i.e., knowledge and awareness) were developed to assess mental health knowledge and awareness. The two outcome variables in this study were mental health knowledge level and awareness level. The cut-off value was taken as 80% of the total scores of both the knowledge and awareness scales and divided into higher and lower groups. Data were analyzed using different descriptive statistical tools and binary logistic regression model. We found more than half (62.1%) of the students had higher knowledge, and 85.1% of the students had a higher awareness of mental health problems. Female students (OR 1.41, 95% confidence interval (CI): 1.15–1.72) and students managing their expenses by personal income and family support were significantly positively associated with the high knowledge of the mental health (OR 1.79, 95% CI: 1.40–2.29). Similarly, age (OR 1.47, 95% CI: 1.01–2.14) was significantly associated with high awareness. Good mental health was significantly negatively associated with the high knowledge (OR 0.72, 95% CI: 0.6–0.87) and positively associated with the high awareness (OR 1.48, 95% CI: 1.15–1.91). Although mental health awareness is high among Bangladeshi university students, knowledge of mental health is insufficient. As a result, it is essential to comprehend the gaps in knowledge and awareness of mental health disorders, as well as how they are addressed.