Drug–target interaction (DTI) prediction plays a fundamental role in modern drug discovery and precision medicine by identifying potential interactions between therapeutic compounds and biological targets. Conventional experimental methods for DTI identification are often time-consuming, expensive, and resource-intensive, limiting the efficiency of early-stage drug development. Computational approaches have therefore emerged as valuable tools for accelerating the discovery of candidate drug–target pairs and supporting precision drug delivery strategies. Recent advances in deep learning have demonstrated significant potential for extracting complex relationships from large-scale biological datasets. However, many deep learning models operate as black-box systems, providing limited insight into the factors influencing prediction outcomes. This paper presents an Explainable Deep Learning Framework (EDLF) for predicting drug–target interactions using molecular and protein sequence information. The proposed framework integrates feature representation, deep neural network-based prediction, and explainable artificial intelligence techniques to generate both accurate and interpretable interaction predictions. Drug molecular descriptors and protein sequence embeddings are utilized as input features for a deep learning architecture designed to estimate interaction probabilities. To improve transparency, Shapley Additive Explanations (SHAP) are incorporated to quantify feature contributions and identify the factors influencing prediction outcomes. Experimental evaluation is conducted using publicly available drug–target interaction datasets. Performance is assessed using accuracy, precision, recall, F1-score, and receiver operating characteristic area under the curve (ROC-AUC). The results indicate that the proposed framework achieves strong predictive performance while maintaining interpretability. The study demonstrates that explainable deep learning models can support computational drug discovery and provide meaningful insights for precision drug delivery research.