Advances in artificial intelligence (AI) and intelligent computing have significantly accelerated drug discovery by enabling accurate modeling of complex biomedical relationships. Among these efforts, drug repositioning—identifying novel therapeutic uses for approved or investigational drugs—offers a cost-effective and time-efficient alternative to de novo drug development. While non-negative matrix factorization (NMF) has been widely adopted for uncovering latent drug–disease associations, conventional implementations often neglect the biological context that underpins these relationships. In this work, we propose a novel NMF-based drug repositioning model that incorporates biological context (NMFIBC), which integrates drug and disease similarity networks through graph-regularized optimization to enhance predictive performance. This design enhances both the robustness and interpretability of association prediction. Extensive benchmarking on multiple gold-standard datasets demonstrates that NMFIBC outperforms existing methods across a range of metrics, including AUC, precision, and F1-score. Moreover, case studies involving clinically relevant drugs validate the biological plausibility of the predicted associations using public databases such as DrugBank, CTD, and KEGG. The proposed framework provides a powerful, context-aware AI strategy for discovering actionable insights in drug repositioning research.