We propose VISO-Grasp, a novel vision-language-informed system designed to systematically address visibility constraints for grasping in severely occluded environments. By leveraging Foundation Models (FMs) for spatial reasoning and active view planning, our framework constructs and updates an instance-centric representation of spatial relationships, enhancing grasp success under challenging occlusions. Furthermore, this representation facilitates active Next-Best-View (NBV) planning and optimizes sequential grasping strategies when direct grasping is infeasible. Additionally, we introduce a multi-view uncertainty-driven grasp fusion mechanism that refines grasp confidence and directional uncertainty in real-time, ensuring robust and stable grasp execution. Extensive real-world experiments demonstrate that VISO-Grasp achieves a success rate of $87.5\%$ in target-oriented grasping with the fewest grasp attempts outperforming baselines. To the best of our knowledge, VISO-Grasp is the first unified framework integrating FMs into target-aware active view planning and 6-DoF grasping in environments with severe occlusions and entire invisibility constraints.