This study investigated the relationship between subjective grip strength and physical function in community-dwelling older women. Subjective grip strength was assessed using a questionnaire, and physical function and body composition were compared between groups with strong and weak subjective grip strength. Additionally, the two groups were compared in those with mild cognitive impairment (MCI) and those with normal cognitive function, respectively. The results showed significant differences in grip strength (p < 0.001), 30 s chair–stand (CS-30) test (p = 0.039), timed up-and-go (TUG) test (p = 0.027), maximal gait speed (p = 0.029), and skeletal muscle mass (p < 0.001). Older adults with normal cognitive function showed significant differences in grip strength (p < 0.001), quadriceps muscle strength (p < 0.009), one-leg standing time (p = 0.041), CS-30 (p = 0.002), TUG (p = 0.014), gait speed (p = 0.006), and skeletal muscle mass (p = 0.003). Older adults with low subjective grip strength had lower physical function and skeletal muscle mass. However, no items showed significant differences between groups among older adults with MCI. Thus, subjective grip strength is an indicator of an overall decline in physical function and a reduction in skeletal muscle mass in older adults, and cognitive function should be considered when assessing subjective grip strength in older adults.