Background: Smartphone and social media use are an integral part of our daily life. Currently, the impact of excessive smartphone and social media use during the COVID-19 pandemic is poorly understood. The present study aimed to investigate problematic smartphone use (PSPU) and problematic social media use (PSMU) among Bangladeshi college and university students during the COVID-19 pandemic.Methods: A cross-sectional study was carried out involving 5,511 Bangladeshi college and university students (male: 58.9%; mean age: 21.2 years [SD = 1.7]; age range: 18–25) during the social-distancing in the COVID-19 pandemic (July 2020). A self-reported survey containing questions regarding socio-demographic, lifestyle, and home quarantine activities along with four psychometric scales was completed by participants.Results: The mean scores of PSPU and PSMU were 20.8 ± 6.8 (out of 36) and 14.7 ± 4.8 (out of 30). Based on a hierarchical regression analysis, PSPU and PSMU were positively associated with lower age, poor sleep, social media use, watching television, anxiety, and depression. Additionally, PSMU was linked to being female, living with nuclear family, having urban residence, irregular physical exercise, poor engagement with academic studies, and avoiding earning activities, whilst being male, being married, living with lower-income family, and alcohol consumption were linked to PSMU.Conclusions: The findings indicate that PSPU and PSMU were linked to poor psychological well-being (i.e., anxiety and depression) and other factors (especially lower age, poor sleep) during the pandemic, further suggesting the need for interventions including virtual awareness programs among college and university students.