An adequate level of health literacy is essential for clear communication between patients and health care workers. The internationalization of universities is increasing in the field of health care. The aims of our research were to measure (1) the level of health literacy and its correlation among university students and (2) the relationship between the different instruments measuring health literacy. A cross-sectional study was conducted in the 2020/2021 academic year. The questionnaire included questions on sociodemographic status, study data, health status, and health literacy level. According to the HLS-EU-Q16 health literacy questionnaire, more than half of the students had a limited HL level in disease prevention (52.4%) and health promotion (58.4%) subindexes. Nationality was found to be an influencing factor ( < 0.001). According to the NVS, 80.1% of the students had an adequate HL level. A significant correlation was found between the results and nationality ( = 0.005). None of the Chew questions demonstrated a correlation with nationality (q1 = 0.269, q2 = 0.368, q3 = 0.528). Nationality is a key factor in the level of subjective and functional health literacy. We need to measure both types of levels to see the real results.