Medications with anticholinergic and sedative properties, even when used in isolation, can negatively impact the physical performance of older adults. Managing complex pharmacological regimens in potentially multimorbid patients remains a significant challenge. This study aimed to examine the association between medication burden, as measured by the Drug Burden Index (DBI), and both postural balance and recent falls in community-dwelling older adults. Medication use was assessed through a structured questionnaire covering both prescribed and over-the-counter drugs taken chronically. The DBI was then calculated. Postural balance was evaluated using a BIOMEC400 force platform during a one-legged stance, and fall events over the previous six months were recorded. The sample consisted of 179 participants from a university outpatient clinic; 70.8% were female and 60.0% were white. A total of 75 participants (41.9%) had a low or high medication burden. These individuals demonstrated significantly worse balance across all parameters (Kruskal–Wallis test, p < 0.05). Additionally, medication burden was strongly associated with recent falls (Chi-square test for trend = 34.1, p < 0.0001). ROC curve analysis identified a DBI cut-off point of 0.5 as being associated with impaired balance. In conclusion, a DBI above 0.5 appears to increase the risk of balance impairment and falls in older adults. The DBI may therefore be a useful public health tool to identify high-risk individuals and support safer medication use in this population.