The present study aimed to assess various stressful situations and the psychological impact of the first COVID-19 pandemic lockdown among youths in Switzerland. We included samples of 1627 young adults aged 19–24 from the Swiss Youth Epidemiological Study on Mental Health and 1146 children and adolescents aged 12–17 years and their parents. We assessed symptoms of various mental health problems, internet use, and perceived stress during the first COVID-19 lockdown. In the analyses, data were weighted to be representative of the Swiss population. During the first lockdown in Switzerland, the most common sources of perceived stress were the disruption of social life and important activities, uncertainty about how long the state of affairs would last, and the pandemic itself. In addition, around one-fifth of the young adults met the criteria for at least one of the mental health problems (attention deficit hyperactivity disorder, depression, generalized anxiety disorder), while one-third of children/adolescents screened positive for at least one of the mental health problems (attention deficit hyperactivity disorder, oppositional defiant disorder, depression, anxiety). Moreover, 30.1% of children and 21.3% of young adults met the criteria for problematic internet use. The study showed considerable stress perceived by young adults and symptoms of mental health problems, especially among females, during the first COVID-19 lockdown in Switzerland.