Although 3D shape completion facilitates robotic grasping from partial observations, deterministic completion models overlook regional uncertainty, which can result in suboptimal grasp poses. To address this limitation, we propose an uncertainty-aware robotic grasping framework that couples geometric completion confidence with physical constraints. The framework integrates a Multi-rate Dropout Ensemble (MDE) into the shape completion network, enabling it to restore 3D geometry while simultaneously quantifying epistemic uncertainty. The quantified uncertainty is then mapped onto a 3D gripper bounding box to evaluate the local reliability of each grasp candidate. Evaluations in simulation on a diverse set of unseen objects demonstrate that our approach effectively suppresses unreliable grasp hypotheses. Overall, the framework significantly reduces geometric reconstruction errors and improves grasping success rates, confirming its strong generalization capability and operational safety under occlusion.