The student population has been highly vulnerable to the risk of mental health deterioration during the coronavirus disease (COVID-19) pandemic. This study aimed to reveal the prevalence and predictors of mental health among students in Poland, Slovenia, Czechia, Ukraine, Russia, Germany, Turkey, Israel, and Colombia in a socioeconomic context during the COVID-19 pandemic. The study was conducted among 2349 students (69% women) from May–July 2020. Data were collected by means of the Generalized Anxiety Disorder (GAD-7), Patient Health Questionnaire (PHQ-8), Perceived Stress Scale (PSS-10), Gender Inequality Index (GII), Standard & Poor’s Global Ratings, the Oxford COVID-19 Government Response Tracker (OxCGRT), and a sociodemographic survey. Descriptive statistics and Bayesian multilevel skew-normal regression analyses were conducted. The prevalence of high stress, depression, and generalized anxiety symptoms in the total sample was 61.30%, 40.3%, and 30%, respectively. The multilevel Bayesian model showed that female sex was a credible predictor of PSS-10, GAD-7, and PHQ-8 scores. In addition, place of residence (town) and educational level (first-cycle studies) were risk factors for the PHQ-8. This study showed that mental health issues are alarming in the student population. Regular psychological support should be provided to students by universities.