The current pandemic of the novel coronavirus COVID-19 has increased the anxiety and fear experienced by many. The main objective of this study was to analyze the psychometric properties of the Spanish-translated version of the Fear of COVID-19 Scale (FCV-19S) using a sample of population in Peru. This is a cross-sectional instrumental study. Data were collected by a convenience sampling method, resulting in a total of 832 participants, and the collection took place over 1 week, April 17–23, 2020. The original version of the FCV-19S was translated from English into Spanish. The results support a bifactor model consisting of one general factor and two specific factors—one of emotional fear reactions and another of somatic expressions of fear of COVID-19 (CFI = 0.988, RMSEA = 0.075). Invariance between healthcare workers and age groups was reached (ΔCFI < 0.01), but the invariance between men and women was not met (ΔCFI = 0.02). Convergent validity was found with depressive, anxious, and posttraumatic stress symptoms. The general factor of the fear of COVID-19 and two specific factors had an optimal level of internal consistency (ω > 0.89 and α > 0.83). The study found the Spanish-translated version of the FCV-19S has good psychometric properties and presents evidence of validity and reliability.