3D neuroimages provide a comprehensive view of brain structure and function, aiding in precise localization and functional connectivity analysis. Segmentation of white matter (WM) tracts using 3D neuroimages is vital for understanding the brain's structural connectivity in both healthy and diseased states. One-shot Class Incremental Semantic Segmentation (OCIS) refers to effectively segmenting new (novel) classes using only a single sample while retaining knowledge of old (base) classes without forgetting. Voxel-contrastive OCIS methods adjust the feature space to alleviate the feature overlap problem between the base and novel classes. However, since WM tract segmentation is a multi-label segmentation task, existing single-label voxel contrastive-based methods may cause inherent contradictions. To address this, we propose a new multi-label voxel contrast framework called MultiCo3D for one-shot class incremental tract segmentation. Our method utilizes uncertainty distillation to preserve base tract segmentation knowledge while adjusting the feature space with multi-label voxel contrast to alleviate feature overlap when learning novel tracts and dynamically weighting multi losses to balance overall loss. We compare our method against several state-of-the-art (SOTA) approaches. The experimental results show that our method significantly enhances one-shot class incremental tract segmentation accuracy across five different experimental setups on HCP and Preto datasets.