Existing 3D instance segmentation methods typically assume that all semantic classes to be segmented would be available during training and only seen categories are segmented at inference. We argue that such a closed-world assumption is restrictive and explore for the first time 3D indoor instance segmentation in an open-world setting, where the model is allowed to distinguish a set of known classes as well as identify an unknown object as unknown and then later incrementally learning the semantic category of the unknown when the corresponding category labels are available. To this end, we introduce an open-world 3D indoor instance segmentation method, where an auto-labeling scheme is employed to produce pseudo-labels during training and induce separation to separate known and unknown category labels. We further improve the pseudo-labels quality at inference by adjusting the unknown class probability based on the objectness score distribution. We also introduce carefully curated open-world splits leveraging realistic scenarios based on inherent object distribution, region-based indoor scene exploration and randomness aspect of open-world classes. Extensive experiments reveal the efficacy of the proposed contributions leading to promising open-world 3D instance segmentation performance. Code and splits are available at: https://github.com/aminebdj/3D-OWIS.