(1) Background: The objective of the present study was to determine the ability of the SARC-F questionnaire to identify individuals at risk of falling among middle-aged and older community-dwelling postmenopausal women. (2) Methods: An analytical cross-sectional study was conducted on 157 women (70.80 ± 8.37 years). The SARC-F questionnaire was used to screen for risk of sarcopenia. Fear of falling and balance confidence, as measured by the Falls Efficacy Scale-International (FES-I) and the Activities-Specific balance Scale-16 items (ABC-16) respectively, were used to assess risk of falling. Anxiety and depression (Hospital Anxiety and Depression Scale), fatigue (Fatigue Severity Scale), body mass index, waist-to-hip ratio, and sleep duration were also determined. (3) Results: Logistic regression showed that higher risk of falling as assessed by FES-I was associated with higher SARC-F scores (OR = 1.656), anxiety levels (OR = 1.147), and age (OR = 1.060), while increased SARC-F scores (OR = 1.612), fatigue (OR = 1.044), and shorter sleep duration (OR = 0.75) were related to ABC-16 scores. In addition, a SARC-F cutoff of 1.50 (83.33% sensitivity and 59.13% specificity) and 3.50 (44.44% sensitivity and 89.26% specificity) were shown to be able to discriminate participants at risk of falling according to the FES-I and the ABC-16, respectively. (4) Conclusions: our results show that SARC-F is an independent predictor of the risk of falling among middle-aged and older community-dwelling postmenopausal women.