The aim of the present study was two-fold: Firstly, to estimate the prevalence of psychological distress among international students at a Hungarian university two years after the COVID-19 outbreak; and secondly, to identify its demographic and socioeconomic factors, with special regard to the students’ food-security status. A cross-sectional study using a self-administered questionnaire was carried out from 27 March to 3 July 2022 among international students at the University of Debrecen. The questionnaire included information on demographic and socioeconomic characteristics, food-security status (six-item United States Department of Agriculture Food Security Survey Module (USDA-FSSM)), and psychological distress (Depression, Anxiety and Stress Scale (DASS-21)). Bivariate analysis was conducted to examine the potential associations between demographic/socioeconomic factors and psychological distress. Additionally, multiple logistic regression was employed to further analyze these associations. Of 398 participants, 42.2%, 48.7%, and 29.4% reported mild to extremely severe depression, anxiety, and stress, respectively. The ages 18–24 (AOR = 2.619; 95% CI: 1.206–5.689) and 25–29 (AOR = 2.663; 95% CI: 1.159–6.119), reporting a low perception of health status (AOR = 1.726; 95% CI: 1.081–2.755), and being food insecure (AOR = 1.984; 95% CI: 1.274–3.090) were significantly associated with depressive symptoms. Being female (AOR = 1.674; 95% CI: 1.090–2.571), reporting a low perception of health status (AOR = 1.736; 95% CI: 1.098–2.744), and being food insecure (AOR = 2.047; 95% CI: 1.327–3.157) were significantly associated with anxiety symptoms. Furthermore, being female (AOR = 1.702; 95% CI: 1.026–2.824)), living with roommates (AOR = 1.977; 95% CI: 1.075–3.635), reporting a low perception of health status (AOR = 2.840; 95% CI: 1.678–4.807), and being food insecure (AOR = 2.295; 95% CI:1.398–3.767) were significantly associated with symptoms of stress. Psychosocial programs combined with strategies to alleviate food insecurity are required to enhance international students’ mental health and well-being.