Deep generative modeling has a strong potential to accelerate drug design. However, existing generative models often face challenges in generalization due to limited data, leading to less innovative designs and unfavorable interactions with target proteins. To address these issues, we propose an interaction-aware 3D molecular generative framework with its conditional generative model named DeepICL. By leveraging the universal nature of protein-ligand interactions, our model can achieve a generalizable structure-based drug design even with a small experimental dataset. Our framework's generalization ability is comprehensively assessed by analyzing generated ligands for unseen targets in terms of binding pose stability, affinity, geometric patterns, diversity, and novelty. The successful design of mutant-selective inhibitors further manifests the impact of our interaction-aware conditional generation approach in real-world applications.