Mental health problems in students are considered a public health challenge. We assessed the prevalence of depression, anxiety, and stress (DAS) with the DASS-21, as well as associated factors, among university students in Bangladesh early in the COVID-19 outbreak. We hypothesized high levels of DAS and their associations with previously reported factors (e.g., poor sleep, lack of exercise, heavy internet use) and those linked to disadvantage (e.g., low monthly family income). We also enquired about participants' satisfaction with their pursuit of their academic studies while living under COVID-19 restrictions. An internet-based survey was conducted during the month of April 2020, involving 3,122 Bangladeshi university students aged 18 to 29 years (59.5% males; mean age 21.4±2 years). Prevalence estimates of depression, anxiety and stress were, respectively, 76.1%, 71.5% and 70.1% for at least mild symptoms, 62.9%, 63.6% and 58.6% for at least moderate symptoms, 35.2%, 40.3%, and 37.7% for at least severe symptoms and 19.7%, 27.5% and 16.5% for at least very severe symptoms. The present estimates of DAS were more prevalent than in previous pre-COVID-19 studies among Bangladeshi university students. Regression analyses with DASS-21-score as a dependent variable revealed associations with factors mostly as hypothesized. The largest effect size on DAS symptoms was related to students' satisfaction with their academic studies during the pandemic. As this survey used cross-sectional and self-reported methods, causality cannot be inferred. Mental health monitoring of students attempting to cope with the impacts of the COVID-19 outbreak may be useful and feasible.