Most studies on the coronavirus pandemic focus on clinical aspects of the COVID-19 disease. However, less attention is paid to other health aspects of the pandemic. The aim of this study was to assess the relationship between the coronavirus pandemic (risk of infection by virus together with associated measures taken to combat it), and the occurrence of a wide range of psychosomatic symptoms and to explore if there is any factor that plays a role in this association. We collected data from a sample of Czech adults (n = 1431) and measured the occurrence of nine health complaints, respondents’ experience during the pandemic and sociodemographic characteristics. The results showed associations between the coronavirus pandemic and increased psychosomatic symptoms and negative emotions. We further found higher risks of increased health complaints in younger people and women. It is also possible that there is higher risk of increased health complaints for respondents with secondary school education, students, and highly spiritual people, but this relationship has to be further investigated. In contrast, respondents with their highest achieved education level being secondary school graduation had a lower risk of increased frequency of stomach-ache. We also found that more negative emotions could increase the frequency of health complaints. Our findings suggest that the coronavirus pandemic and associated government measures could have a significant influence on the prevalence of health complaints and emotional state.