Depth map super-resolution technology aims to improve the spatial resolution of low-resolution depth maps and effectively restore high-frequency detail information. Traditional convolutional neural network has limitations in dealing with long-range dependencies and are unable to fully model the global contextual information in depth maps. Although transformer can model global dependencies, its computational complexity and memory consumption are quadratic, which significantly limits its ability to process high-resolution depth maps. In this paper, we propose a multi-scale fusion U-shaped Mamba (MSF-UM) model, a novel guided depth map super-resolution framework. The core innovation of this model is to integrate Mamba's efficient state-space modeling capabilities into a multi-scale U-shaped fusion structure guided by a color image. The structure combining the residual dense channel attention block and the Mamba state space module is designed, which combines the local feature extraction capability of the convolutional layer with the modeling advantage of the state space model for long-distance dependencies. At the same time, the model adopts a multi-scale cross-modal fusion strategy to make full use of the high-frequency texture information from the color image to guide the super-resolution process of the depth map. Compared with existing mainstream methods, the proposed MSF-UM significantly reduces the number of model parameters while achieving better reconstruction accuracy. Extensive experiments on multiple publicly available datasets validate the effectiveness of the model, especially showing excellent generalization ability in the task of large-scale depth map super-resolution.