This study explores the psychosocial impact of the COVID-19 pandemic on the population in Greece during the general lockdown period. Specifically, depression, anxiety and stress scores, as well as the factors associated with vulnerability to developing mental health conditions during this period, were investigated. A total of 911 adults participated in an online survey by completing a self-reporting questionnaire that included demographic questions, DASS-42 items (anxiety, stress and depression scales) and other questions related to personal experience. Regression modelling uncovered a significant relationship between gender and DASS scores, with women having significantly higher scores than men for all mental health problems. Participants aged 20–39 years were especially vulnerable to experiencing poor mental health. Unemployed participants reported having worse mental health than others. Having more perceived psychosocial support during the pandemic was associated with lower overall scores. Thus, women, young adults and the unemployed exhibited particularly high levels of vulnerability, while individuals who received social support from relatives and friends during the lockdown were more resilient to the effects of social isolation.