The COVID-19 pandemic affects individuals' mental health that can result in fear of getting COVID-19 infection and depression. As there is no prior study available, we evaluated these mental health outcomes and associated factors among the general population and healthcare professionals (HCPs) in Bangladesh. This nationwide cross-sectional study comprised 3388 individuals including 834 HCPs. The measures included socio-demographics, healthcare, and patient-care related information, the Bangla Patient Health Questionnaire, and the Bangla Fear of COVID-19 Scale. Multiple linear regression analyses were performed to identify risk factors. Just over one-quarter of the participants were depressed, and was significantly associated with COVID-19 fear. Regression analyses showed that, both in general population and HCPs, depression and fear of COVID-19 were strongly predicted by being female; however, depression was inversely associated with being married. Particularly, among the HCPs, being restless while examining a patient with flu-like symptoms and while examining a patient returning from abroad was found to be significant predictor for both depression and fear of COVID-19. HCPs who were using single protective equipment for a week had greater depression and those who felt insecure due to the pandemic had a high level of COVID-19 fear. The findings identified major psychological impacts among the participants, suggesting the urgent need to promote mental wellbeing in both general population and medical professionals.