Background: Communication skills (CSs) and evidence-based practice (EBP) are key foundations for offering personalized and quality nursing care. CS that results in open communication is fundamental for applying EBP. Objectives: The objective of the study was to assess the relationship between the acquisition of EBP competencies and learning CS after taking an EBP course in the nursing degree. Methods: Pre-test-post-test quasi-experimental study without a control group. The study population comprised fourth-year undergraduate nursing students. Before and after an EBP course, students completed a questionnaire on CS competence (HP-CSS) and EBP competence (EBP-COQ). The EBP course lasts for 15 weeks, with 150 h of work for the student. Out of these 150 h, 60 are conducted in person, while the remaining 90 h are for independent or group work, utilizing the flipped classroom methodology. Bivariate, correlational, pairwise Student’s t-test, and linear regression multivariate analyses were performed. Results: The sample was composed of 153 students. After completing the EBP course, there was a statistically significant improvement in informative communication (p = 0.046) and assertiveness (p = 0.018). However, there were no observed changes in empathy, respect, and the total score of the CS competence. The results from the multivariate analysis showed that the dimensions of attitude towards EBP and EBP knowledge had a positive relation to three of the four dimensions of the CS and overall competence. Regarding the students’ variables and characteristics, admission through special programs for athletes and older students (p < 0.001) and being female (p = 0.004) were positively statistically associated with empathy. Conclusions: EBP training positively affects the development of CS in nursing students, as shown by significant improvements in the total scores of the CS and the dimensions of informative communication and assertiveness after the intervention. This study demonstrates the initial applicability and usefulness of an EBP training program for the development of CS in nursing students.