Background/Objectives: Breast cancer remains the most common malignancy among women worldwide, with many patients experiencing persistent psychological symptoms that extend beyond active treatment. Among these, sleep disturbances, anxiety, and depression frequently co-occur and can significantly impair quality of life and treatment adherence. This study aimed to assess the prevalence of poor sleep quality and examine its associations with anxiety and depression in a large cohort of Turkish women with breast cancer. Additionally, the study sought to identify sociodemographic and clinical predictors of sleep disturbance. Methods: In this cross-sectional study, 601 women with histologically confirmed breast cancer who were undergoing or had completed active treatment were recruited from a tertiary oncology center in Turkey between January 2023 and December 2023. The mean age of participants was 54 years (range 25–83). More than half of the patients were postmenopausal (56.3%), and 6% had stage IV disease. Sleep quality and psychological distress were assessed using the Pittsburgh Sleep Quality Index (PSQI) and the Hospital Anxiety and Depression Scale (HADS). Descriptive statistics, correlation analyses, and multivariate regression models were employed to identify significant predictors. Results: Poor sleep quality (PSQI > 5) was identified in 33.2% of participants. Patients with poor sleep reported significantly higher anxiety and depression scores (p < 0.001). Multivariate analysis revealed that being single, having children, undergoing breast-conserving surgery, and elevated anxiety scores were independent predictors of poor sleep. Additionally, marital status, menopausal status, and treatment modality were significantly associated with anxiety and depression scores. Conclusions: One-third of Turkish breast cancer patients experience clinically relevant sleep disturbances, which are strongly linked to psychological distress, particularly anxiety. These findings underscore the importance of incorporating routine psychological screening into oncologic care and highlight the need for individualized psychosocial support strategies that aim to improve both emotional well-being and overall clinical outcomes.