The recent COVID-19 pandemic has imposed threats on both physical and mental health since its outbreak. This study aimed to explore the impact of the COVID-19 pandemic on mental health among a representative sample of home-quarantined Bangladeshi adults. A cross-sectional design was used with an online survey completed by a convenience sample recruited via social media. A total of 1,427 respondents were recruited, and their mental health was assessed by the DASS-21 measure. The prevalence of anxiety symptoms and depressive symptoms was 33.7% and 57.9%, respectively, and 59.7% reported mild to extremely severe levels of stress. Perceptions that the pandemic disrupted life events, affected mental health, jobs, the economy and education, predictions of a worsening situation, and uncertainty of the health care system capacities were significantly associated with poor mental health outcomes. Multivariate logistic regressions showed that sociodemographic factors and perceptions of COVID-19 significantly predict mental health outcomes. These findings warrant the consideration of easily accessible low-intensity mental health interventions during and beyond this pandemic.