Background: Since 2012, education standards in medical faculties in Poland have allowed medical universities to introduce content related to multiculturalism. On the one hand, this creates a necessity to introduce new strategies, forms, and techniques of education aimed at the development of knowledge, skills, and attitudes in terms of multiculturalism. On the other hand, there is a need to evaluate their effects. The main goal of this study was to evaluate the cultural competence and cultural intelligence of master’s degree nursing students before the commencement of and two months after cultural education training in the form of the intercultural communication workshops included in the study program. Methods: The following questionnaires were used in the study: the Cross-Cultural Competence Inventory (CCCI) and the Cultural Intelligence Scale (CQS). Two consecutive classes (2019 and 2020) of master’s nursing students were tested twice (pre-test, post-test). The study was conducted at a leading medical university that educates nurses at a master’s level in Poland. In total, 130 master’s nursing students took part in this evaluative study: 64 individuals in 2019 (study 1) and 66 individuals in 2020 (study 2). Results: In comparison to the pre-test, the post-test showed that the surveyed students in both study 1 and study 2 obtained significantly higher overall results in terms of cultural intelligence (p = 0.001; p = 0.004, respectively) as well as in the behavioral (p = 0.001; p = 0.002) and cognitive (p = 0.001; p = 0.008, respectively) subscales. The cultural competence results were also higher overall, but the difference was insignificant. Conclusions: The study shows the efficiency of training/workshops in the development of culturally specific knowledge and cultural intervention skills. At the same time, it postulates the need to plan and organize cultural education programs in a form that aims to improve the development of culturally sensitive attitudes.