Background: Menopause is a natural biological process frequently associated with sleep disturbances due to hormonal changes. Poor sleep quality during the postmenopausal period adversely affects physical health, psychological well-being, and overall quality of life. Although pharmacological treatments are commonly used, their limitations highlight the need for safe and cost-effective non-pharmacological interventions. Objective: To assess the effectiveness of Brain Gym exercises on sleep quality in postmenopausal women. Methodology: A quasi-experimental study was conducted over a period of four weeks among 30 postmenopausal women aged 45–65 years with poor sleep quality (Pittsburgh Sleep Quality Index [PSQI] > 5). Participants were selected through community-based screening. Baseline sleep quality was assessed using the PSQI questionnaire. Brain Gym exercises were demonstrated by a qualified physiotherapist and practiced daily for 15–20 minutes for four weeks. Post-intervention PSQI scores were reassessed. Data were analyzed using descriptive statistics, Spearman’s rho correlation, and paired t-test. Results: The mean PSQI score reduced from 6.87 ± 1.69 before intervention to 6.23 ± 1.63 after the intervention. Paired t-test analysis showed a statistically significant improvement in sleep quality (p = 0.00018). Spearman’s rho analysis revealed a weak correlation between age and sleep quality scores, while a strong positive correlation was observed between pre- and post-intervention PSQI scores (ρ = 0.86, p < 0.05). Conclusion: Brain Gym exercises resulted in a modest but statistically significant improvement in sleep quality among postmenopausal women and may be considered a safe, cost-effective, complementary intervention for managing menopausal sleep disturbances.