Customer churn remains a critical challenge for the telecommunications industry because customer attrition directly affects revenue, customer lifetime value, and long-term business sustainability. Accurate prediction of customers at risk of leaving is therefore essential for developing proactive retention strategies. This study proposes a hybrid wrapper-based feature selection framework that integrates Genetic Algorithm (GA) with Extreme Gradient Boosting (XGBoost) to improve customer churn prediction using the Telco Customer Churn Dataset. The proposed framework employs GA to identify the most informative feature subset through an evolutionary search process, followed by XGBoost classification on the optimized feature space. The novelty of this study lies in applying GA explicitly as a wrapper-based feature selection mechanism, rather than for hyperparameter optimization, enabling XGBoost to learn from a compact and highly discriminative set of customer attributes. Experimental results demonstrate that the proposed GA-XGBoost framework reduces feature dimensionality while achieving higher predictive performance than standalone XGBoost and several widely used machine learning classifiers under identical experimental conditions. These findings indicate that evolutionary feature optimization effectively enhances classification performance while reducing model complexity. The proposed framework provides a practical and computationally efficient solution for supporting data-driven customer retention strategies, enabling telecommunications providers to identify high-risk customers more accurately and optimize targeted retention campaigns.