Previous studies reported a significant association between postural control and lower-limb strength of several muscle groups, however, they were focused especially on knee muscles and ankle plantar and dorsal flexors. The aim of the present study is to examine the correlation between the muscle strength of ankle invertors, evertors, plantar flexors, and dorsal flexors and the control of bipedal stance in young and older adults. Thirty one young (aged 22.8 ± 2.6 years) and thirty one older adults (aged 70.5 ± 7.2 years) voluntarily participated in this study. Ankle muscle strength was evaluated by an isokinetic dynamometer. Normalized peak torque and work were averaged for four repetitions and for both lower limbs. The control of bipedal stance was evaluated by the sample entropy derived from an accelerometer placed on the lumbar spine while the subject stood on a foam pad with eyes open. Results showed significant age-related differences in ankle muscle strength and sample entropy in medial-lateral direction. More interestingly, the correlation between ankle muscle strength and the sample entropy was significantly different between young and older adults. Indeed, no significant correlation was observed in the younger adults. Conversely, in the older adults, the work of the ankle evertors positively correlated with sample entropy in the medial-lateral direction during bipedal stance (r = 0.36), whereas the peak torque and work of the dorsal flexors were significantly correlated with sample entropy in the anterior-posterior direction during bipedal stance (r = 0.44 for both variables). In the young adults, results suggest that, standing on foam with eyes open is a relatively easy postural task that does not require the full ankle muscle strength capacity. Taken together, the present findings suggest that older adults have a different association between ankle muscle strength and the sample entropy during bipedal stance.