Introduction and objective: The main aim of this study was to provide indicators of mental health in the Polish population and to examine the need for different kinds of support (psychological, financial, educational, work-related, etc.) during the first phase of the COVID-19 pandemic. Materials and methods: The study used demographic measures and questions specific to the COVID-19 pandemic. The General Functioning Questionnaire (GFQ-58) and the State-Trait Anxiety Inventory (STAI) were used to assess mental health and psychosomatic functioning. Additionally, participants selected psychological and somatic symptoms they experienced. Results: Participants reported numerous psychological and somatic symptoms associated with the COVID-19 pandemic. Stepwise regression analyses revealed significant predictors of mental health, anxiety, and psychological/somatic symptoms. Risk indicators included current psychiatric treatment, prior psychiatric history, receiving psychiatric or psychological treatment during the pandemic, limitations in interpersonal contacts and physical activity, need for financial assistance, need for support at work and in education, unemployment, and female sex. There were many specific sex differences, but women generally reported higher intensity of psychological/somatic symptoms. Women experienced symptoms directly linked to the pandemic, whereas men experienced the consequences of the pandemic in a more indirect way. They did not openly attribute their symptoms to the pandemic; however, its consequences affected men’s mental health and general psychosocial functioning to a greater extent. Conclusions: The COVID-19 pandemic has had a substantial impact on general psychosomatic functioning, but this impact differs for women and men. It is possible to identify specific risk indicators which are responsible for reduced mental health during the COVID-19 pandemic.