This letter presents a novel self-supervised learning strategy to improve the robustness of a monocular depth estimation (MDE) network against motion blur. Motion blur, a common problem in real-world applications such as autonomous driving and scene reconstruction, often hinders accurate depth perception. Conventional MDE methods are effective under controlled conditions but struggle to generalise their performance to blurred images. To address this problem, we generate blur-synthesized data to train a blur-robust MDE model without the need for preprocessing such as deblurring. By incorporating self-distillation techniques and using blur-synthesised data, we significantly enhance depth estimation accuracy for blurred images without any additional computational or memory overhead. Extensive experimental results demonstrate the effectiveness of the proposed method, enhancing existing MDE models to accurately estimate depth information across various blur conditions.