The objective was to evaluate the associations of psychological distress and sleep quality with balance confidence, muscle strength, and functional balance among community-dwelling middle-aged and older people. An analytical cross-sectional study was conducted (n = 304). Balance confidence (Activities-specific Balance Confidence scale, ABC), muscle strength (hand grip dynamometer), and functional balance (Timed Up-and-Go test) were assessed. Psychological distress and sleep quality were evaluated by the Hospital Anxiety and Depression Scale and the Pittsburgh Sleep Quality Index, respectively. Age, sex, physical activity level, nutritional status, and fatigue were included as possible confounders. Multivariate linear and logistic regressions were performed. Higher values of anxiety (OR = 1.10), fatigue (OR = 1.04), and older age (OR = 1.08) were associated with an increased risk of falling (ABC < 67%). Greater muscle strength was associated with male sex and improved nutritional status (adjusted R2 = 0.39). On the other hand, being older and using sleeping medication were linked to poorer functional balance (adjusted R2 = 0.115). In conclusion, greater anxiety levels and the use of sleep medication were linked to a high risk of falling and poorer functional balance, respectively. No associations were found between muscle strength and sleep quality, anxiety, or depression.