Service robots operating in unstructured environments must effectively recognize and segment unknown objects to enhance their functionality. Traditional supervised learning-based segmentation techniques require extensive annotated datasets, which are impractical for the diversity of objects encountered in real-world scenarios. Unseen object instance segmentation (UOIS) methods aim to address this by training models on synthetic data to generalize to novel objects, but they often suffer from the simulation-to-reality gap. This article proposes a novel approach (ZISVFM) for solving UOIS by leveraging the powerful zero-shot capability of the segment anything model (SAM) and explicit visual representations from a self-supervised vision transformer (ViT). The proposed framework operates in the following three stages: generating object-agnostic mask proposals from colorized depth images using SAM, refining these proposals using attention-based features from the self-supervised ViT to filter nonobject masks, and applying K-Medoids clustering to generate point prompts that guide SAM toward precise object segmentation. Experimental validation on two benchmark datasets and a self-collected dataset demonstrates the superior performance of ZISVFM in complex environments, including hierarchical settings such as cabinets, drawers, and handheld objects.