Open-vocabulary 3D instance segmentation seeks to segment and classify instances beyond the annotated label space. Existing methods typically map 3D instances to 2D RGB-D images, and then employ vision-language models (VLMs) for classification. However, such a mapping strategy usually introduces noise from 2D occlusions and incurs substantial computational and memory costs during inference, slowing down the inference speed. To address the above problems, we propose a Fast Open-vocabulary 3D instance segmentation method via Label-guided Knowledge distillation (FOLK). Our core idea is to design a teacher model that extracts high-quality instance embeddings and distills its open-vocabulary knowledge into a 3D student model. In this way, during inference, the distilled 3D model can directly classify instances from the 3D point cloud, avoiding noise caused by occlusions and significantly accelerating the inference process. Specifically, we first design a teacher model to generate a 2D CLIP embedding for each 3D instance, incorporating both visibility and viewpoint diversity, which serves as the learning target for distillation. We then develop a 3D student model that directly produces a 3D embedding for each 3D instance. During training, we propose a label-guided distillation algorithm to distill open-vocabulary knowledge from label-consistent 2D embeddings into the student model. FOLK conducted experiments on the ScanNet200 and Replica datasets, achieving state-of-the-art performance on the ScanNet200 dataset with an AP50 score of 35.7, while running approximately 6.0x to 152.2x faster than previous methods. All codes will be released after the paper is accepted.