Abstract Background Greater muscle mass can generally produce greater muscle strength. However, whether higher muscle mass is associated with higher muscle quality (muscle strength relative to muscle mass) remains unknown. Furthermore, the nature of this relationship, and how their interaction determines the presence of functional impairments are unknown. This article aims to address these issues. Methods Secondary data analysis including 1219 women aged 75 years and older of the Toulouse ÉPIDemiologie de l'OSteoporose cohort study. Body composition (dual energy X-ray absorptiometry), handgrip, and knee extension strength were assessed. Physical function was measured using the chair stand test as well as the usual and fast gait speed tests. Participants were also asked if they experienced any difficulty in performing functional tasks. Results Upper- and lower-body muscle quality (r = −0.42, P < .001 and r = −0.16, P < .001, respectively) were significantly and negatively correlated with appendicular skeletal muscle mass index (ASMI). Independently of ASMI, individuals with high muscle quality had low risks of functional impairments (odds ratio <0.74), whereas individuals with high ASMI but low muscle quality had high risks of impairments (odds ratio >1.27). Conclusions This inverse relationship between muscle mass and quality implies that sarcopenic individuals have better muscle quality than nonsarcopenic individuals. Results also suggest that high muscle quality may compensate for low ASMI with respect to functional impairments. Physical activity may potentially be involved in this relationship.