Gait, dynamic balance, and functional mobility problems are well-known fall risk factors. Furthermore, sleep disturbances, anxiety, and depression are prevalent among older women. This study aimed to analyze the associations of sleep quality, anxiety, and depression with functional mobility, gait speed, and dynamic balance in community-dwelling postmenopausal women aged ≥ 60 years. A total of 271 women (69.18 ± 5.69 years) participated in this study. Functional mobility (Timed Up-and-Go Test), dynamic balance (3-meter tandem walk test), gait speed (OptoGait® optical detection system), sleep quality (Pittsburgh Sleep Quality Index), and anxiety and depression (Hospital Anxiety and Depression Scale) were assessed. Our results showed that poor sleep efficiency and the use of sleeping medication were related to decreased gait speed (R2 = 0.072). Poor functional mobility was linked to depression and the use of sleeping medication (R2 = 0.159). Additionally, increased symptoms of anxiety and depression were associated with worsened dynamic balance (R2 = 0.127). In conclusion, poorer sleep quality is associated with slower gait speed and reduced functional mobility, which is also related, along with impaired dynamic balance, to higher levels of anxiety and depression.