Object instance segmentation is a key challenge for indoor robots navigating cluttered environments with many small objects. Limitations in 3D sensing capabilities often make it difficult to detect every possible object. While deep learning approaches may be effective for this problem, manually annotating 3D data for supervised learning is time-consuming. In this work, we explore zero-shot instance segmentation (ZSIS) from RGB-D data to identify unseen objects in a semantic category-agnostic manner. We introduce a zero-shot split for Tabletop Objects Dataset (TOD-Z) to enable this study and present a method that uses annotated objects to learn the ``objectness'' of pixels and generalize to unseen object categories in cluttered indoor environments. Our method, SupeRGB-D, groups pixels into small patches based on geometric cues and learns to merge the patches in a deep agglomerative clustering fashion. SupeRGB-D outperforms existing baselines on unseen objects while achieving similar performance on seen objects. Additionally, it is extremely lightweight (0.4 MB memory requirement) and suitable for mobile and robotic applications. The dataset split and code will be made publicly available upon acceptance.