The Coronavirus Disease of 2019 (COVID-19) pandemic has threatened the global economy, livelihoods, and physical and mental health since it began in 2019. This study aimed to examine how the COVID-19 pandemic affected the mental health of a representative sample of Bangladeshi youth and to identify the influencing factors. Through social media, 390 people were asked to participate in an online survey using the cross-sectional methodology. The chi-square test was used to examine the associations between the status of mental health and other variables. It was found that because of the lockdown, 59.3% and 21% of the participants were severely and moderately affected in terms of mental health, respectively. Poor mental health outcomes are strongly associated with family status, profession, marital status, avoiding shaking hands, cleaning and disinfecting objects and surfaces which are frequently used, knowledgeable community, impact on livelihood, food availability, routine behavior, impact on education, and impact on mental health. A multinomial logistic regression (MLR) model with 95% confidence interval (CI) with a p-value < 0.05 was used to determine the effect of explanatory variables on the adjusted odds ratio (AOR) of mental health status. The results of MLR showed that age, marital status, the risk of participants of their family members getting sick from COVID-19, impact on wages, physical and mental abuse, closed schools, etc., significantly predicted mental health outcomes. This study facilitated a deeper understanding of mental health during the COVID-19 outbreak.