Problematic use of Internet (PUI) and problematic use of Facebook (PUF) has been linked to escalating behavioral health issues among university students and has increased during the COVID-19 pandemic. This study estimated the prevalence of and explored associated factors for PUI and PUF among Bangladeshi university students during the COVID-19 pandemic. A cross-sectional online survey was undertaken among 1101 Bangladeshi university students between November and December 2020. The Internet Addiction Test and Facebook Addiction Scale were used to assess PIU and PUF, respectively. A multiple linear regression analysis was performed to adjust for confounders. Among the participants, PUI and PUF were found in 39.3% and 37.1%, respectively. The multiple linear regression model indicated PUI was significantly associated with participants residing in a village, arts majors, those unsatisfied with their major, having mediocre parental relationships, failure in romantic relationships, physical comorbidities, longer use of the Internet, using the Internet for purposes other than education, using social media, and downloading movies/TV series. PUF was significantly associated with village residence, lower income, arts majors, failure in romantic relationships, longer use of the Internet, using the Internet for purposes other than education, and downloading movies/TV series. Both PUI and PUF have been prevalent among Bangladeshi university students during the COVID-19 pandemic. Longitudinal & exploratory studies are warranted in the future to identify causal factors for PUI and PUF and appropriate interventions should be designed quickly for this population.