Structural Health Monitoring (SHM) is essential for ensuring the safety, durability, and operational efficiency of civil infrastructure. However, modern sensing systems often involve numerous sensors, leading to high-dimensional data that increases computational complexity and hinders interpretability. This study proposes a Shapley Additive Explanations (SHAP)-based feature selection framework to identify the most informative sensors for structural damage classification using a one-dimensional convolutional neural network (1D CNN). The approach is applied to the ASCE benchmark structure dataset, where SHAP is used to select the top 8 sensors out of 12, significantly reducing input dimensionality while improving classification performance. To validate the effectiveness of SHAP, comparative experiments were conducted using Principal Component Analysis (PCA), Mutual Information (MI), and the ANOVA F-test. Results are evaluated through stratified three-fold cross-validation using metrics such as accuracy, F1 score, and AUC. The performance of the 1D CNN in integration with SHAP-based feature selection not only achieves superior classification metrics but also outperforms the model using all 12 sensors as well as those based on other feature selection strategies. Specifically, the SHAP-based 1D-CNN model, using only 8 sensors, achieved an overall accuracy of 98.58%, F1 score of 98.22%, and AUC of 99.89%, outperforming the performance of 1D-CNN considering all 12 sensors.