Background: Levels of fear have increased since the COVID-19 pandemic outbreak. The absence of a safe and effective vaccine for mass-vaccination deteriorates this situation, which has a significant impact on mental health. This study aimed to assess the feelings of fear among nurses and nursing students in five European countries. Methods: A multicenter cross-sectional study was conducted in five European countries (Greece, Albania, Cyprus, Spain, and Kosovo) before the start of mass vaccination in Europe. Data collection was conducted in December 2020–January 2021 using an online questionnaire for nursing students and professional nurses. Fear of COVID-19 Scale (FCV-19S) was used for measuring levels of fear. IBM SPSS version 21.0 was used for statistical analysis. Results: The study population included 1135 nurses and 1920 nursing students from Kosovo (n = 1085), Spain (n = 663), Greece (n = 534), Albania (n = 529), and Cyprus (n = 244). According to multivariable analysis, females (OR = 2.53, 95% CI = 1.89–3.15), married (OR = 0.86, 95% CI = 0.24–1.48), nurses (OR = 0.87, 95% CI = 0.28–1.45) and those with a chronic disease (OR = 0.86, 95% CI = 0.11–1.62) were more fearful of COVID-19. Conclusions: It is important to decrease fear in the population of nurses who are at the frontlines of the pandemic. The provision of appropriate education and training activities for nurses and students to manage their stress levels is of high importance. Future studies should focus on levels of fear after the administration of several safe and effective vaccines worldwide.