Video Semantic Segmentation (VSS) involves assigning a semantic label to each pixel in a video sequence. Prior work in this field has demonstrated promising results by extending image semantic segmentation models to exploit temporal relationships across video frames; however, these approaches often incur significant computational costs. In this paper, we propose an efficient mask propagation framework for VSS, called MPVSS. Our approach first employs a strong query-based image segmentor on sparse key frames to generate accurate binary masks and class predictions. We then design a flow estimation module utilizing the learned queries to generate a set of segment-aware flow maps, each associated with a mask prediction from the key frame. Finally, the mask-flow pairs are warped to serve as the mask predictions for the non-key frames. By reusing predictions from key frames, we circumvent the need to process a large volume of video frames individually with resource-intensive segmentors, alleviating temporal redundancy and significantly reducing computational costs. Extensive experiments on VSPW and Cityscapes demonstrate that our mask propagation framework achieves SOTA accuracy and efficiency trade-offs. For instance, our best model with Swin-L backbone outperforms the SOTA MRCFA using MiT-B5 by 4.0% mIoU, requiring only 26% FLOPs on the VSPW dataset. Moreover, our framework reduces up to 4x FLOPs compared to the per-frame Mask2Former baseline with only up to 2% mIoU degradation on the Cityscapes validation set. Code is available at https://github.com/ziplab/MPVSS.