Laboratory mice, particularly the C57BL/6 strain, are essential animal models in biomedical research. However, accurate 3D surface motion reconstruction of mice remains a significant challenge due to their complex non-rigid deformations, textureless fur-covered surfaces, and the lack of realistic 3D mesh models. Moreover, existing visual datasets for mice reconstruction only contain sparse viewpoints without 3D geometries. To fill the gap, we introduce MoReMouse, the first monocular dense 3D reconstruction network specifically designed for C57BL/6 mice. To achieve high-fidelity 3D reconstructions, we present three key innovations. First, we create the first high-fidelity, dense-view synthetic dataset for C57BL/6 mice by rendering a realistic, anatomically accurate Gaussian mouse avatar. Second, MoReMouse leverages a transformer-based feedforward architecture combined with triplane representation, enabling high-quality 3D surface generation from a single image, optimized for the intricacies of small animal morphology. Third, we propose geodesic-based continuous correspondence embeddings on the mouse surface, which serve as strong semantic priors, improving surface consistency and reconstruction stability, especially in highly dynamic regions like limbs and tail. Through extensive quantitative and qualitative evaluations, we demonstrate that MoReMouse significantly outperforms existing open-source methods in both accuracy and robustness.