Appropriate studies on drug–drug interactions (DDIs) can evade possible adverse side effects due to the ingestion of multiple drugs. This paper proposes a novel framework called Similarity Network Fusion and Hybrid Convolutional Neural Network (SNF–HCNN) to predict the DDIs better. The proposed framework leverages data from DrugBank, PubChem, and SIDER. Seven critical drug features are extracted: Target, Transporter, Enzymes, Chemical substructure, Carrier, Offside, and Side effects. The Jaccard Similarity measure evaluates the similarity of drug features to construct a comprehensive similarity matrix that effectively captures potential drug relationships and patterns. The similarity selection process identifies the most relevant features, reduces redundancy, and enhances identifying potential drug interactions. Integrating Similarity Network Fusion (SNF) with the selected similarity matrix ensures a comprehensive representation of drug features and leads to superior accuracy compared to conventional methods. Our experimental results demonstrate the effectiveness of the proposed hybrid convolutional neural network (HCNN) architectures, such as CNN+LR (CNN+Logistic Regression), CNN+RF (CNN+Random Forest), and CNN+SVM (CNN+Support Vector Machine), showing impressive accuracies of 95.19%, 94.45%, and 93.65%, respectively. Moreover, CNN+LR outperforms other approaches regarding precision, sensitivity, F1-score, and AUC score, which implicate better outcomes for ensuring medication safety aspects in clinical settings in the future.