Fear of coronavirus disease 2019 (COVID-19) is one of the main psychological impacts of the actual pandemic, especially among the population groups with higher mortality rates. The Fear of COVID-19 Scale (FCV-19S) has been used in different scenarios to assess fear associated with COVID-19, but this has not been done frequently in people living in long-term care (LTC) settings. The present study is aimed at measuring the psychometric properties of the Spanish version of the FCV-19S in residents in LTC settings, following both the classical test theory (CTT) and Rasch model frameworks. The participants (n = 447), aged 60 years or older, were asked to complete the FCV-19S and to report, among other issues, their levels of depression, resilience, emotional wellbeing and health-related quality of life with validated scales. The mean FCV-19S score was 18.36 (SD 8.28, range 7–35), with higher scores for women, participants with lower education (primary or less) and higher adherence to preventive measures (all, p < 0.05). The Cronbach’s alpha for the FCV-19S was 0.94. After eliminating two items due to a lack of fit, the FCV-19S showed a good fit to the Rasch model (χ2 (20) = 30.24, p = 0.019, PSI = 0.87), with unidimensionality (binomial 95% CI 0.001 to 0.045) and item local independency. Question 5 showed differential item functioning by sex. The present study shows that the FCV-19S has satisfactory reliability and validity, which supports its use to effectively measure fear in older people living in LTC settings. This tool could help identify risk groups that may need specific health education and effective communication strategies to lower fear levels. This might have a beneficial impact on adherence to preventive measures.