Background: The SARS-Cov-2 pandemic has had a profound impact on all aspects of life in the global population, causing above other, psychological problems. Aims: The objective of this study was to evaluate the mental health of the Poles during the COVID-19 pandemic. Methods: A prospective, cross-sectional web-based survey design was adopted. The study horizon was from 1 June 2021, to 31 December 2021. An anonymous, standardized questionnaire was disseminated electronically by means of social media among Polish adults. The following tests were performed: Depression, Anxiety, and Stress Scale (DASS-21), and the Insomnia Severity Index (ISI). Results: A total of 1306 individuals completed the survey. Of the participants, 77.79% were female at a mean age of 34.89 ± (14.79), 62.25% had higher education, and 56.43% were employed. The prevalence of depression, anxiety, stress, and sleep disturbances in this sample were as follows: 50.38%, 43.49%, 61.26%, and 44.74%, respectively. Poor self-estimated health status, the presence of comorbidities, and regular use of nicotine significantly increased the risk of any of the analyzed psychiatric symptoms and sleep disorders. The depression level was significantly associated with age, living alone, health status, and the use of nicotine. Moreover, the level of anxiety was significantly associated with age and health status. The level of stress depended on gender, age, health status, use of nicotine, and being vaccinated against SARS-CoV-2. Sleep disturbances depended on age, health status, the presence of comorbidities, and regular use of drugs. Conclusions: The Polish population manifested numerous psychological symptoms during the COVID-19 pandemic. There is a need to afford psychological support to them and ensure their mental health.