Objective Previous studies highlighted a high prevalence of mental health issues among students during the COVID-19 pandemic, but there is no evidence from Russia. This study was aimed to examine the prevalence of somatic and psychological distress among Russian university students. Method The cross-sectional study was conducted in March-April 2021. The participants were university students from several regions of Russia (N = 1236). The Patient Health Questionnaire-15 and Depression, Anxiety, and Stress Scales-21 were used to measure the somatic and psychological distress. Results The prevalence of somatic burden, depression, anxiety, and stress was 72.2%, 54.7%, 63.4%, and 55.4%, respectively. Somatic burden, anxiety, and stress were more frequently observed in females and students with experience of COVID-19 disease compared to males and students without experience of COVID-19 disease. Conclusions These data illuminate the high prevalence and potential risk factors for somatic and psychological distress among Russian university students and determine the importance of psychoeducation and preventive measures in the Russian university environment.