Studying in college can be a challenging time for many students, which can affect their mental health. In addition to academic pressure and stressful tasks, another aggravating factor in student life is the ongoing coronavirus disease 2019 (COVID-19) pandemic. The aim of the study was to examine the prevalence of anxiety, depression, and somatic symptoms in Czech and Slovak college students during the COVID-19 pandemic and to evaluate possible socio-demographic determinants of mental health problems. A total of 3,099 respondents participated in this cross-sectional study (Czech Republic: 1,422, Slovakia: 1,677). The analyzes included the Patient Health Questionnaire for somatic symptoms (PHQ-15), the Generalized Anxiety Disorder instrument (GAD-7), and the Patient Health Questionnaire for depression (PHQ-9). Socio-demographic factors were gender, age, family structure, marital status, form of study, degree of study, year of study, field of study, distance between home and college, residence, and housing during the semester. Among Czech students, prevalence of somatic complaints, anxiety and depression was 72.2, 40.3, and 52%, respectively. Among Slovak students, prevalence of somatic complaints, anxiety and depression was 69.5, 34.6, and 47%, respectively. During the COVID-19 pandemic, the most severe mental health problems were identified in a non-negligible part of the sample (Czech Republic: PHQ-15 = 10.1%, GAD-7 = 4.9%, PHQ-9 = 3.4%; Slovakia: PHQ-15 = 7.4%, GAD-7 = 3.5%, PHQ-9 = 2.7%). Regarding the differences between the analyzed countries, a significantly higher score in somatic symptoms, anxiety, and depression was identified in the Czech Republic. Significant differences in mental disorders were found in most socio-demographic characteristics. The main results of the logistic regression analysis revealed that risk factors for mental health disorders in Czech and Slovak students were female gender, younger age, third degree of study, and study of Informatics, Mathematics, Information and Communication Technologies (ICT). Especially in the case of these high-risk groups of students, public policies should consider a response to impending problems. The findings are an appeal for a proactive approach to improving the mental health of students and for the implementation of effective prevention programs, which are more than necessary in the Czech and Slovak college environment.