•The prevalence of Facebook addiction was 36.9%.•FA was 1.67 and 2.51 times higher among the students with depressive symptoms and a domestic violence history respectively.•Participants who did not fail or fall into love were less likely to be at risk of FA than those who did.•Appropriate behavioral interventions targeting these factors should be envisaged to reduce FA among university students. Facebook addiction (FA) has been suggested as a potential behavioral addiction. Data about FA among university students in Bangladesh has been scarce despite being a research topic of growing interest. This study aimed to determine the prevalence of FA and its related factors amongst university students in Bangladesh. A cross-sectional study was conducted between February to March 2020 within two Bangladeshi universities (i.e., Patuakhali Science and Technology University and Barishal University) residing in the southern territory of the country. Data were collected on socio-demographic characteristics, behavioral and online activities. The Bergen Facebook Addiction Scale and the Beck Depression Inventory-21 Scale were used to access the risk of FA, and depressive symptoms of students. About 36.9% of the students were identified as at risk of Facebook addiction using 18 as the cutoff score out of 30 on the Bergen Facebook Addiction Scale. The risk factors of Facebook addiction were predicted to be failure in love, having history of domestic violence, having stressful life event, sufferings from sleep disturbance (i.e., more than 8 h sleep status compared to 6–8 h normal status), spending more than 5 h daily time on Facebook, and having symptoms of depression. Future research should use longitudinal designs to identify FA contributing factors among university students in Bangladesh.