Prior and ongoing COVID-19 pandemic restrictions have resulted in substantial changes to everyday life. The pandemic and measures of its control affect mental health negatively. Self-reported data from 15,375 participants from 23 countries were collected from May to August 2020 during the early phases of the COVID-19 pandemic. Two questionnaires measuring anxiety level were used in this study—the Generalized Anxiety Disorder Scale (GAD-7), and the State Anxiety Inventory (SAI). The associations between a set of social indicators on anxiety during COVID-19 (e.g., sex, age, country, live alone) were tested as well. Self-reported anxiety during the first wave of the COVID-19 pandemic varied across countries, with the maximum levels reported for Brazil, Canada, Italy, Iraq and the USA. Sex differences of anxiety levels during COVID-19 were also examined, and results showed women reported higher levels of anxiety compared to men. Overall, our results demonstrated that the self-reported symptoms of anxiety were higher compared to those reported in general before pandemic. We conclude that such cultural dimensions as individualism/collectivism, power distance and looseness/tightness may function as protective adaptive mechanisms against the development of anxiety disorders in a pandemic situation.