This study aimed to describe the impact of the COVID-19 pandemic on the social situation, self-perceived health status, and mental well-being of adolescents in Catalonia during home confinement, and to evaluate factors that are associated with poor overall mental well-being. An online cross-sectional study among a cohort of students (14–18 years old) of central Catalonia (DESKcohort) was performed during June–July 2020. Poisson regression models with robust variance were used to identify variables associated with “poor overall well-being,” measured by the short version of the Warwick–Edinburgh Mental Wellbeing Scale. Out of 303 participants, 42.1% reported a decrease in family income, and 32.8% a loss of parental employment due to the COVID-19 pandemic, and these percentages were higher among people living in low socioeconomic neighborhoods (53.3% and 43.2%, respectively). Overall, 56.8% presented a poor overall well-being. Participants reporting a decrease in their family’s income (aPR = 1.33) and those knowing a close person or family who died of COVID-19 (aPR = 1.42) were more likely to report a poor overall well-being. This study highlights the patterns of inequality and social vulnerability for COVID-19 pandemic outcomes. Considering social inequalities, interventions are needed to mitigate the impact of COVID-19 pandemic on the physical and the psychological wellbeing of children and their families.