We introduce uncertainty-aware object instance segmentation (UncOS) and demonstrate its usefulness for embodied interactive segmentation. To deal with uncertainty in robot perception, we propose a method for generating a hypothesis distribution of object segmentation. We obtain a set of region-factored segmentation hypotheses together with confidence estimates by making multiple queries of large pre-trained models. This process can produce segmentation results that achieve state-of-the-art performance on unseen object segmentation problems. The output can also serve as input to a belief-driven process for selecting robot actions to perturb the scene to reduce ambiguity. We demonstrate the effectiveness of this method in real-robot experiments. Website: https://sites.google.com/view/embodied-uncertain-seg