Social distancing plays a leading role in controlling the spread of coronavirus. However, prolonged lockdown can lead to negative consequences in terms of mental health. The goal of the research is to examine the relationship between anxiety and general psychosomatic functioning during the COVID-19 pandemic; the impact of psychological flexibility and mindfulness is also considered. Variables were measured with self-report questionnaires and symptom checklists. The sample included 170 people (M = 27.79, SD = 8.16). Pearson’s correlation, stepwise regression, and path analysis were conducted. The results showed a significant positive relationship between state anxiety and somatic and psychological responses to the pandemic. Path analysis revealed that mindfulness had a direct negative impact on and decreased the level of state anxiety (b = −0.22, p = 0.002), whereas psychological flexibility influenced the variable indirectly (b = 0.23, p = 0.002) by enhancing psychosomatic functioning (b = −0.64, p < 0.001). Psychological flexibility and mindfulness may mediate the development of mental disorders and facilitate achieving overall wellbeing. The study points to the usefulness of mindfulness practice as a form of self-help with anxiety symptoms; this is crucial during the pandemic because contact with clients is restricted.