Students’ severe affective mental distress has emerged as significant public health attention globally because of the disastrous effects of coronavirus disease 2019 (COVID-19). The current study aimed at exploring the prevalence of two alarming psychological distresses, depression and anxiety, among university students following a prolonged shutdown of educational institutions in Bangladesh. A cross-sectional online-based study was conducted by deploying two standard scales to assess the depression and anxiety among Bangladeshi students from various universities amid the 2^nd stream of the COVID-19 pandemic. A total of 568 Bangladeshi university students participated in this questionnaire-based survey through various social media platforms. Frequency and percentage distribution as univariate, chi-square (χ²) test as bivariate, and logistic regression as multivariate analyses were applied to investigate the prevalence of depression and anxiety and their associated various sociodemographic factors. After cleaning and eliminating the partial data, we analyzed 465 responses, where 42% were female and 64.3% were from public universities. Both mental disorders were prevalent in more than 50% of Bangladeshi university students. The students from the private universities were two times and 2.7 times more depressed and anxious, respectively than the students from the public universities. In addition, the students who became incomeless had significantly more anxiety (adjusted odds ratio [AOR] = 1.711; p = 0.018) than those who did not lose income source during the COVID-19 lockdown. The present study revealed that more than 50% of Bangladeshi university students were suffering from depression and anxiety. Several effective measures must be assured by the concerted efforts of university authorities, educationalists, and the Government to alleviate these distressing mental health burdens.